Quantum Optics - Science topic

There is a difference between AI and quantum computing.

For AI you only need normal computers.

Quantum computers have still a very far way to go,

even in advanced labs.

Must use very low temperature and need high stability.

Interestingly, your first half of the question addresses the con the Google acheived "quantum supremacy" some years back by quantum computing some 10^48 data bits of random zeroes and ones. the claim went on to say that conventional computers would take 10,000 years to generate 10^48 bits of randome zeroes and ones.

Obviously, this means that this stated test result must then require 10,000 years to validate. As such, Googles claim cannot be validated. Point being that if each data set requires conventional computers to validate, then what is the point of non validated "quantum computed" data?

Quantum Computing and certainly Quantum Teleportation of data and Information is all scam. you publosh news headlines and faux scientific papers purely to dance on Wall Street. And in all that Commerce, you find Lamborghinis, Ferraris, Aston Martins, and a lab that looks like an old black and white film filled with antiquated and equipment so obsolete, you cannot even run it with a 21st century computer: used junk for the xameras.

many thanks for your help, i'll investigate both and see how i get on. Neil

Thank you Harri

I supposed it would go as you describe. Good to hear it by experimentalists. I am a little afraid that when using a mask (fibers even more) diffraction can spread my rays but I suppose it would be negligible as the holes would not be to narrow but at 1-2 mm.

Regards: Ilian

PS. By the way what is the easiest practical way to rotate polarization from V to H. Can you recommend a rotator of polarization? Of course sugar water solutions can do but I look for something more compact.

The biggest number to be factored is 35, by quantum computing achieved on IBM’s Quantum Computer (https://arxiv.org/abs/1903.00768).

35 is a 6-bit number, so we are far away from 2048 bit RSA keys (which has 617 decimal digits – compared to these 2 digits!!!)

In fact most people surely burst out laughing at this tiny number…

Leonid Vesselov Thank you very much.

Ahmed Mounaf Mahdi, it is not just the "quality and accuracy of the sources" that GPT provides that are an issue. A source cited by GPT can be entirely ficticious, i.e. might not exist. And even if you challenge GPT about the accuracy, it may not reply with a true statement.

See e.g.

Time-bin encoding is a technique used in quantum information science to encode a qubit of information on a photon. Quantum information science makes use of qubits as a basic resource similar to bits in classical computing. Qubits are any two-level quantum mechanical system; there are many different physical implementations of qubits, one of which is time-bin encoding.

I know I am a year late, but I wanted to explain the way I understand it for anyone else having the same question. This is also pretty much Miccola's answer with more details.

The most generic formula for interference visibility is V=Amplitude/Average of your signal's intensity. Normally, this is for wave interference but it takes a different form when you measure single photon interference (which is what the HOM measures).

If your signal is oscillating (similar to a sine/cosine function), then your Amplitude=(Max-Min)/2, and your Average=(Max+Min)/2. Hence, interference Visibility=(Max-Min)/(Max+Min). This is the typical formula for wave interference.

On the other hand, in a HOM measurement, your coincidence detection drops due to the HOM effect only when the delay between events is ~0. This behavior is similar to a delta function. In this case, your Amplitude=Max-Min (the depth of your valley), and your Average≅Max (since the coincidences are consistently at their Max except for a small area near the zero delay). Hence, HOM Visibility=(Max-Min)/Max.

I would suggest to verify the temporal synchronization of the two detectors. For a too narrow coincidence window and different latency of the detectors, the true coincidences might be outside of the coincidence window. Only false (random) coincidences are present. The first step would be to increase the coincidence window to dozens of ns to surely cover any difference in latency. Then you can start decreasing the coincidence window and adding a delay to the fastest detector channel, e.g. using time tagger functionality or simply extending the length of a coaxial cable.

Also, it might be useful to add cut-off filters transmitting the red signal and stopping the blue pump in front of the detectors. Using the filters you make sure that your signal comes from the SPDC process and not from the laser. Filters https://www.semrock.com/filterdetails.aspx?id=blp01-633r-25 are very good but you can use any low-cost alternative.

@All

Please discuss the importance of wave function and energy level on entropy and followed by non- locality .

Dear I Chavdarovski,

Whenever you want to detect which slit the photon or electron is passing through, you loose the double slit interference pattern.

This is the same statement as before.

Whatever detector you use, once the photon or electron is detected by the detector , the original path or the propagation is lost and the pattern vanishes.

Thanks

N Das

The problem doesn't seem difficult.

If you don't like the red boxing effect, you can modified the hyperref macro package as

\usepackage[colorlinks = true, linkcolor = blue, urlcolor = blue, citecolor = blue, anchorcolor = blue]{hyperref}

As for the line spacing question, you can add

\renewcommand{\baselinestretch}{2.0}

adjust the numbers according to your needs.

You may have a look at http://www.qphotonics.com/Wavelength-Stabilized-Laser-Diodes/

In the question I asked for a reference to solving operator equations, even better would be examples of solving such equations.

This answer provides another example of solving a simple "operator equation". It again concerns a quantum mechanical simple harmonic oscillator but this time an operator equation for one of the 'Quadrature Operators' is solved. Please see the two attachments

There are two proofs now, associated with this question.These two proofs are about expressing time dependent Heisenberg picture operators in terms of functions of the time and time independent Schrodinger picture operators.

In the future I may collect these proofs together and form a project update containing them, see my 'Quantum Optics' project.

I get a different result to Zweibach [1], see 'Quantum Dynamics.pdf' the first line of equation (3.44). Hopefully I have not made a silly mistake (a sign is different) if I have, hopefully it's toward the end of the proof.

Reference 1,

Prof Barton Zwiebach. 8.05 Quantum Physics II. Fall 2013. Massachusetts Institute of Technology: MIT OpenCourseWare, https://ocw.mit.edu/. License: Creative Commons BY-NC-SA.

Also

Reach 'Quantum Dynamics.pdf' from

Main course page at

Thank you Barry Fleagle for your contribution.

It sounds to me like the optical field spatial distribution which appears in a recent submission to the 2020 OSA Frontiers in Optics titled "Optical illusions of single-photon measurements" that I couldn't present online and I'm not sure whether it was included in the proceedings. But a copy is available on ResearchGate.

My main goal was, however, to do with the Bell-type nonlocality which is physically highly questionable because the same correlation function can be derived for single and independent qubits of polarization as is commonly done for entangled qubits. The latter are destroyed by the quantum Rayleigh scattering through spontaneous emission in the case of a single photon per radiation mode. There is a submission titled "The Scattering and Disappearance of Entangled Photons in a Homogeneous Dielectric Medium,” Rochester Conference on Coherence and Quantum Optics (CQO-11), doi.org/10.1364/CQO.2019.M5A.19.

Dear Pavel Gostev, I should add to all interesting answers in this thread that in the limit of large α, the statistics of a coherent state is equivalent to that of a classical stable wave, I elaborate:

The coherent state by definition is an eigenstate of the annihilation operator in the Heisenberg picture, and the formal solution of the eigenvalue equation is the vacuum state displaced to a location α in phase space, that is, the unitary displacement operator D(α) operate on the vacuum. So as a conclusion I guess that a state with infinite photon distribution is a classical wave.

Non-hermitian means that the operator does not have its self-adjoint:

T \ne T*

Without a self-adjoint, there is a missing symmetry and unitarity in operations in Hilbert or Banach space. The solutions are therefore complex, and the eigenvalues also. Such eigenvalues have therefore no direct physical meaning, unless they are either scaled by some complex number (see Nimrod Moiseyev works), or the operator is made self-adjoint in a bounded domain where it gives real eigenvalues.

Yes, we have H coils in three directions. However, minimizing the external magnetic field is manipulated by any change in the frequency shifts of cooling beam and so on.

Dear Dimitry,

it may be possible to used the system proposed in:

to determine if entangled photons are generated by biological systems.

many thanks,

Neil

As John F Black points out, LED pumping of single transverse mode fibre lasers is problematic. Coupling efficiency into the core will be low from a spatially incoherent LED source.

Yb co-doping of Er-doped fibre is widely used in a clad-pumped configuration, in which the laser/signal is confined to the core, but pump light is guided in an inner cladding region. This allows pumping by 900-980 nm broad stripe diode lasers which are efficient, but difficult to couple to a single mode waveguide. High output powers and high efficiency are possible.

If your intent is to minimise power dissipation in the diode source, optical quantum efficiency of the laser may not be the best metric. You also need to consider quantum efficiency and wavelength of the diode pump, and coupling efficiency to the laser fibre or cavity. Note that for the same QE and drive current, a 530 nm diode will generally dissipate more power than a 980 nm diode, due to the higher band gap and hence a higher voltage drop.

Yes, certainly i can see that this would be a problem, many thanks for the response.

Neil

Unfortunately, I have no significant information on BBO. I can only imagine, that the story is similar, i.e. several compounds including LN were competing and BBO stayed persisting due to not only its nonlinear coefficient, but a combination of various practical and technical considerations (Growth, stability, etc.) as well.

Zachariasen was a mineralogist by profession, i.e. he studied geology in Oslo. But his work would from todays perspective probably considered solid state physics. He did systematic x-ray diffraction analysis.

His PhD thesis is called " Untersuchungen über die Kristallstruktur von Sesquioxyden und Verbindungen ABO3", which is in german. Translated it means something like: "Investigation on the crystal structure of sequioxides and compounds of ABO3 type". Sesquioxides are materials of the general chemical compounds A2O3, where A could be things like Al and O is oxides, while ABO3 are things like A=Li and B=Nb etc. His thesis is about x-ray diffraction analysis of as many compounds as possible of these groups to find structural rules etc. The only thing you can find online readily are summaries of his thesis:

As far as I understand it, he did grow (or got someone to grow) LiNbO3, as I am not aware of its natural occurence. Early works on the structure of LiNbO3 point to the early works of Zachariasen as early work on the crystal structure. Compare Abrahams for example:

Anyway, the early works by Zachariasen is only an interesting side-note. Zachariasen never noted the polar structure or ferroelectricity. This was noted by Matthias and Reimeka, who noted this:

by the way: While LN is used for nonlinear devices and not really designed for large nonlinear coefficients, there is work trying to optimize compounds for ultra large second order nonliearities or electro-optic coefficients. This has been done for polymers, because in chemistry and with large molecules, there is more flexibility in designing specific properties.

If you just compare the nonlinear coefficients of these molecules with LN, you will find 100 or 1000 times higher nonlinearities easily. By the way, you may now ask, we we are not using nonlinear polymers. People have built extremely efficient nonlinear frequency converters or electro-optic modulators out of this. But polymers have one big issue, which is stability. Large molecules tend to decompose or change their chemical structure under UV light, heat or ambient chemical enviromements. In contrast to this, LN as a crystal stays stable for years. Even domain structures stay stable for years. LN is relatively resistant to scratches, it melts only a way above 1000°C etc. But again, LN is not without its problems. Just search for research directed to address LNs photorefraction (which I think is also one field, where BBO comes in. It takes more power; This is also one of the reasone, why still alternatives are researched, such as KTP). Another limiting factor of LN are the huge mode sizes in indiffused waveguides in bulk samples. This leads to an ultimate limit in its conversion efficiency or requires huge voltages in modulator. However, the advent of thin film LN has addressed this issue. Just compare these two recent articles:

A further issue is the smallest poling period for quasi-phase matching, which can be achieved. Currently there is a lot of interest to get sub-micron domain periods, which can be used for counter-propagating frequency conversion processes. However, this has not yet been shown in LN, however in KTP. Check the work by Canalias:

I hope, I could help you.

Regards,

Michael

Thank you very much for your hint. I understand it now. I was confused when I read inaccurate interpretations in some articles but it's become clear for me now.

Thank You

You can see this related paper @Chathuranga Basnayaka

Stam Nicolis, to the state 2.

If vacuum can cause this decay to other state when the states are not degenerate, I don't know, maybe it can do the same to these two degenate states. If this was a normal problem I could say that this will not happen for degenerate states but I have a sentence for this problem that when I tend the energies of these to states to a certain value, this sentence does not vanish.

Dear Mickey,

If you means physical efficiency it depends upon from the second order nonlinearity which are growing with main frequency while SHG power may decreasing if it is approaching to the nearest absorption band of crystal.

Technical efficiency depends on length of the nonlinear crystal in the phasing direction. This direction is also frequency dependent and very strong. Only the nonlinear crystals with 90-grade phasing do not have similar frequency dependence. If You will have choose nonlinear crystal with taking into account this details You get high efficiency of SHG. 90% efficiency of SHG has been achieved by the so called intracavity location of nonlinear crystal, but this way is connected with application cavity mirrors with the peculiar frequency reflection.

The difference is simply described in the following:

https://www.quora.com/Why-is-a-four-level-laser-more-efficient-than-a-three-level-laser

I'd like to propose a different kind of answer. I think what you're referring to, Mohammad Sayem Mahmood, is an experiment in which Stern-Gerlach apparatuses are arranged in sequence. In this case the following is observed (see also the attached figure taken from wikipedia):

1.If we orient an SG device in the z direction we observe electrons as being deflected up or down.

2. Following that, we can filter out the electrons that have been deflected down. We can then pass the remaining electrons through a second SG device. With this second device also oriented in the z direction we only observe deflections up and never down, as expected. However, If the second SG device is oriented in the x direction then we observe that half of electrons are deflected left and half deflected right.

3. Now we can consider an arrangement with three SG devices. As before the first device is oriented in the z direction and we filter out those electrons that are deflected down. The second device is oriented in the x direction, and we can choose to filter out those that are deflected right, say. Then the third device is oriented in the z direction again.

What might be considered surprising here is that even though we have filtered out electrons that have z spin down, the act of using the second SG device to measure x spin means that when we check z spin once more using the third device half of those electrons passing through are deflected down!

As for an explanation of what is happening here, quantum mechanically the second device acts as a measurement which acts on the state of the system by collapsing it into a state oriented right or a state oriented left. So even though we had filtered to leave only z spin up electrons after the first device, we have now reset these electrons into a state that is unbiased relative to the third SG device; so accordingly we see half of the electrons being deflected up and half down. By invoking measurement invasiveness, via collapse of the wavefunction, we avoid difficulties with interpreting spin as an intrinsic property in this instance.

From a foundational perspective, we might be suspicious of this measurement invasiveness via wavefunction collapse, however. For instance we could take something akin to the perspective of EPR (which in their case was in response to a different kind of experiment) and say that, we might be able to find a more complete theory than Quantum Mechanics, which would nevertheless agree with QMs empirical predictions, but which would describe the electrons passing through the SG devices in a non-invasive way.

A no-go theorem due to Leggett and Garg essentially says that there can be no deeper theory with this property. Another way to interpret the Leggett-Garg result would be that if we insist on describing SG devices as non-invasive then we have a problem with considering spin as an intrinsic non-contextual property of electrons.

(Incidentally, on the Leggett–Garg theorem, I personally found an article by Maroney and Timpson to give a clearer discussion of how to interpret it than the original.)

I find it interesting, too, that you make the link in your question with context. There is also a related feature that can be picked out in the empirical predictions of quantum mechanics, in other kinds of experiments, known as contextuality, which indeed poses problems for our understanding of observable properties being intrinsic to the system of study independent of context of which observables are being observed in conjunction. In fact, in some of my own research I have been looking particularly at the link between contextuality and Leggett–Garg-type results.

You might want to look up articles on coherent LIDAR. Single photon sensitive heterodyne detection is standard practice for that purpose.

Hello,

Do you propose a non-quantum theory for the effect?

Cheers, Ed Gerck

single count of each path multiply the coincidence window you have and multiply your measurement time or accumulation time

People have achieved negative absolute temperatures but that is in nano kelvins by magnetic cooling. However the temperature we refer as zero kelvin is actually a little above absolute zero. So basically the negative temperatures we are talking about a temperature above absolute zero that will radiate for sure. But nobody knows what is the absolute zero but be sure it will be some fractions of kelvin below 0 K. I think getting a temperature even like -1 K is hypothetical.

Sofia

actually its been rather hot here, so im half on holidays.

Forgive my scepticism about entangled particles remaining such

forever. The universe is noisy and quantum phenomena is suceptible

to perturbations.

Regards, juan

Comments concerning (b) and (c): (i) For free particles, momentum is conserved and hence the kinetic energy too is conserved. Therefore, due to coupling with vacuum, the energy of the free particle cannot decrease, unlike the case of bound states. Ergo, entangled free particles are least affected by vacuum fluctuations.

(ii) Certain general statements concerning quantum gravity can still be made like Planck energy cut off, microscopic wormholes, virtual black holes and so on, even in the absence of a proper quantum gravity theory. And papers have been written on their effects on the cosmological constant problem. Please read Weinberg's 1989 review.

Rotating wave approximation is useful when the Hamiltonian of the quantum system has explicit time dependence, such that the system Hamiltonian at two arbitrary different times do not necessarily commute, as a result the Unitary time evolution operator associated cannot be expressed in a simple, closed form, the Dyson series expansion is employed in this situation to construct the zero, first, second and higher order terms of the operator.

Rotating wave approximation is used in NMR spectroscopy, here, the RF linearly oscillating field is visualized as consisting of two circularly oscillating fields, oscillating with the same frequency ( that of the linear field) but in opposite sense, in presence of this RF pulse field, the total NMR spin Hamiltonian has explicit time dependence and is not commuting at different times. By switching over to a rotating frame of reference rotating at the frequency of the Rf feild, one of the circular components becomes stationary in this reference frame and the other appears to oscillate twice as fast, therefore, its contribution to spin evolution is negligible, therefore, the time dependant Scrodinger equation in the rotating reference frame is associated with an Hamiltonian that effectively time independent and hence, the equation for time evolution can be expressed in closed, analytic form.

Dear Muhammad Usman Khan sir,

I have specified question. Can you please give some light on this. I find the paper from which you have taken the abstract. Thanks for this suggestion. I am reading this article.

If you have photons circularly polarized and you want to know if they are right-circular, or left-circular, the direct measurement is through the Beth experiment: the photon is sent upon a very light disk, suspended. The disk rotates according to the direction of circular polarization of the photon.

For more details you can look in

D. N. Moothoo, J. Arlt, R. S. Conroy, F. Akerboom, A. Voit, and K. Dholakiaa, "Beth’s experiment using optical tweezers", Am. J. Phys. 69 (3), March 2001

You can have a look at https://doi.org/10.1016/j.physrep.2006.01.004 for a review of theoretical and experimental aspects of multiphoton quantum optics.

Thanks. Your response  was informative. More  than the unidirectionality, what is interesting is the possibility of varying the transmittance of a particular medium to a particular channel smoothly and in a lossless manner . Of course, in an electrical circuit, the uni-directionality of a circuit (diode etc) help in wave shaping (as in the case of a rectifier)

 What does the meaning of time scale in the x axis and intensity of the peak after the 0 time scale

... at least as it regards the space groups: P3(1)12 and P3(2)12 are the two enantionmorphs. Its works similar with space group pairs containing 64/62 or 41/43. In other cases the two space group types of the enantiomorphs have the same space group type (e.g. P2(1)2(1)2(1))...

Hello there,

Why is this considered as a violation of no-cloning theorem? Coherent state is not a single photon state, and what you do with a beam-splitter is just dividing  the number of photons in half at each port. The cloning definition is different; copying information onto another particle (having two identical particles). In your case, you have many copies and just devide them into two

You can define the Brillouin zone(BZ) as the Fourier transform of the lattice of your material, that is true, but it is hard to understand why is useful only by its definition. In order to understand its use, you need to first understand the Bloch theorem, this theorem state that the spectrum of a infinite periodic system can be described in terms of plane-wave like eigenstates. These eigenstates are labeled by using a quantum number k, which are the points in the Brillouin zone. In this answer that I gave in Quora I explain how it work for graphene https://www.quora.com/How-is-it-that-electrons-act-like-massless-particles-in-graphene

Dear Zahraa, 

You should precise the reasons of your questions so as to answer you efficiently: do you plan to build a DRO (which temporal regime: cw, pulsed?) or do you just require general understanding of DRO operation? Apart from the practical technical conditions briefly summarized above, the physics of doubly-resonant parametric oscillator is quite complex and its implementation depends on the application (single-frequency outputs or not, etc...). DRO's are in principle very unstable in terms of longitudinal mode hopping behaviour and often require active cavity length stabilization. Their main practical (experimental) use are  quantum optics investigations of the physics of twin beams (amplitude noise squeezing, photon entanglements...). For other applied physics applications (e.g. sources for mid-IR laser spectroscopy or other biomedical applications in the mid-IR) singly-resonant oscillators - either in the cw regime for high resolution or in the pulsed ns , ps of fs regime - are preferred for their intrinsic relative frequency stability and tuning behaviour.    

as you asked

Bloch I, Dalibard J, Nascimbene S. Quantum simulations with ultracold quantum gases[J]. Nature Physics, 2012, 8(4): 267-276.

Look at the Sommerfeld problem, which is arguably the simplest conceivable diffraction problem: you consider a two-dimensional system, with a plane wave obliquely incident on a half line. There are 3 different regions in which the behaviour is qualitatively different

1) the reflection region, where the wave is roughly given by a superposition of two waves, one incident, one reflected.

2) the transmission region, in which one wave goes through

3) the shadow region.

The exact solution must account for these 3 different behaviours, and display a continuous transition between all of them. Sommerfeld's solution does exactly that, but it should not be a surprise that, in order to be able to do that, it is fairly complicated. 

Yes indeed, this length is defined that way in textbooks. This means that beyond that length, if the beam still traverses the material, photons will split back into two fundamental longer wavelength... and then vice versa...

The topological charge of a pulsed laser beam can be measured by interfering the vortex beam with a reference beam that has a flat phase. The number of nodes in the interference pattern is a measurement of the OAM in the vortex beam.

See the following article: G Gariepy et al. Creating High-Harmonic Beams with Controlled Orbital Angular Momentum

No.

It's a very good question, very direct, and I'm going to follow it.

Christopher, I meant the same when talking about the sensitivity of detectors. Under the word "detector" I meant a device capable of distinguishing between polarization like you said

Sure.

"Is there any experiment to measure the time of pattern appearance?"

I think the integration time depends on (1) the intensity of the light source used and (2) on the desired signal/noise ratio for the experiment. So it depends on the specifics of each experiment.

But you are correct, the interference takes place even at the single photon level. Only a "hard" measurement on a camera or detector collapses the inteference pattern to a particular position.

You may find these articles interesting:

Observing the Average Trajectories of Single Photons in a Two-Slit Interferometer http://doi.org/10.1126/science.1202218

A double-slit 'which-way' experiment on the complementarity–uncertainty debate http://doi.org/10.1088/1367-2630/9/8/287

It makes sense differentiate logically between "polarisation of light" and "spin of a photon". For me this terms are not yet defined true enough in actual Quantum Physics and especially Quantum Optics. Both are real observed and by experiments proved facts but the real movement of a photon - inside of it and in a compound ray - are - for me - not clear too.

Bandwidth (range of frequencies) over which channel is constant is called coherence Bandwidth.

Coherence Bandwidth ~ (1/Maximum Delay Spread)

The better way to calculate coherence bandwidth is using RMS Delay Spread, as different channel will experience different signal intensity over different delay span with same delay spread.

Dear Chethan,

giving a quick look at your input file and to your main problem ( the system doesn't go relaxing because of non-convergence of the energy), I have some suggestions that you can apply in order to fix (hopefully!) your problem:

1) Looking at the PBE Ultrasoft pseudopotential for the Molybdenum, the pseudopotential file suggest to use a "ecutwfc" not less than 48 Ry (where you use 50, which is potentially ok!), but also a "ecutrho" no less than 407. By default "ecutrho" is 4 times ecutwfc (200 Ry in your case, which probably affect negatively the convergence of the energy!): I suggest to increase both "ecutwfc" and "ecutrho" (not specified in your list) to 60 and 430 Ry. The carbon atoms should not be a problem.

2) try to reduce the value of the degauss from 0.001 to 0.01. It will make faster the running with a sufficient good precision.

3) the energy threshold for the convergence "conv_thr" I guess it's too high for having good realistic results. By default is set 1.0E-06. At least, follow this default setting for the convergence.

About the rest, for example the crystal structure, I don't know so much about this compound. I know that there are two phases, alpha and beta with respectively orthorhombic and hexagonal lattice. So, if you know the geometry of the system and the right atomic disposition, you can try to set an appropriate value for "ibrav" and insert the unit cell parameters.

I hope this can be helpful.

Best,

A.

I can't send to you my results, because they are not still published. But it is possible, on tuesday, to speak together via Skype, for example ...

 Dear Ma'am,  

RHS is constant. L1 and L2 are the length of the two cavities and k is wave propagation constant. I have found the solution. That 2m*pi factor is playing a crucial role in the expansion of trigonometric series. Thanks...

Thank you again Eugene.

Are you familiar with the concept of Exclusion Zone (EZ) water? The argument was that water at a hydrophilic interface is bound in place by the strong bonds of the surface. These strengthened bonds then increase the bond strength of water molecules behind the interface layer. The newly strengthened bonds then share bond strength with other water molecules and so the region of bound water increases to the extent that it can be seen as birefringence in a polarised light microscope. I have had to conclude that the original research was misinterpreted.

However, I am looking at ultrasonically induced birefringence. As I understand it, the ultrasonic wave frequency is such that a standing wave is created in the water. The nodal points of the standing wave are relatively fixed in place. Water "stuck" in the nodal points will tend to form their characteristic tetrahedral configuration (as in ice) which should exhibit birefringence. If birefringence is evident then crystalline order is implied.

I value any thoughts you might have on this idea.

Many thanks,

Peter.

Hi Miles,

The scaling as you say it is easy to get doing some approximations, but if you want the exact factors you need to do them numerically. The typical approximations aer: considering the phase matching sinc function as an exponential, and assuming the indices of refraction of the three waves are the same.

If you have a particular problem you want to solve I am happy to share the program that we use with you (or for that matter for anyone interested ;-) )

Cheers,

Gabriel

   Dear Ahmed,

   I strongly agree with your last sentence" go ahead to the forward". And even I would add that it is full of value that there are people able to face difficult new points of views within so stablished and tested theories as classical electrodynamics. My best wishes for Arbab and my remarks only try to help in thinking on weak points of his equations.

you could buy ready made dispensers from

Then you only need to attach them to the vacuum side of an electrical feedthrough.

or, you can make a reservoir by having an ampoule (http://www.sigmaaldrich.com/catalog/product/aldrich/244856?lang=en&region=GB) inside vacuum and once evacuated break it. Then to reach the desired background gas you would have to heat up the reservoir.

There is plenty of literature for both solutions, maybe not so much for K, but you'll find it for Rb wich is quite similar

Hello, 

First, some comments regarding previous postings in this thread:

To the question, yes, the electronic levels of a molecule can be regarded as degrees of freedom such as vibration and rotation, and it may make sense to do so, such as in the final stages of an isotope separation process. However, it is more often the case that the ro-vibrational energy range involved (eg, in the infrared for molecules) is very far from the electronic level energy range of the molecule, so as to make both possible and useful to not consider the electronic levels as a degree of freedom.

Further, the translation energy can also be regarded as a degree of freedom in a molecule, as in photodissociation and Doppler effects. For example of the later, the Doppler effect due to the random velocities of molecules in a gas causes a spectral line broadening that prevents a precise measurement of the line center for a molecule at rest. It can also obscure narrow splittings, for example caused by hyperfine effects, that provide information about the molecular wavefunction.

Cheers, Ed Gerck

Dear Donggyu Jang,

There may be a more intuitive way to explain this, but more mathematically you can think of it in the following way. A closed subshell is an eigenstate of total orbital angular momentum operator squared, L², with the quantum number L=0, so that the eigenvalue L(L+1) is also zero. Similarly, a closed subshell is also an eigenstate of total spin angular momentum operator squared, S²,  with the quantum number S=0 and eigenvalue S(S+1)=0. These two statements can be proven by noting that closed subshells have wavefunctions that are Slater determinants and that closed-shell Slater determinants are invariant under the spatial and spin rotation groups, SO(3) and SU(2), respectively. For more details, see, e.g., the link below. I hope you find this answer useful!

Regards,

Pekko

A lot of good answers here, but I think that the key limitation to the question is that detecting single photons becomes increasingly difficult as the photon energy decreases.  It is possible to detect single microwave photons in circuit QED systems, but I am not aware of any work being done to in-couple the free-space photons into such a system - which would be very hard IMO.  As mentioned several times above, however, the interference effects for long-wavelength photons would exist if the classical interference is seen, so the largest systems would presumably be the very long baseline interferometers used in radio wave detection.  But of course, if you are trying to simultaneously prove the photonic effect, then the single photon energy would be too hard to detect.

I would guess (although I haven't checked) that the lowest energy photons would have been seen with superconducting transition edge detectors.  These can apparently work at least at the THz regime, although I don't know if photon statistics have been observed there or not.  Assuming that the detectors work, then just as @Enrico Sales mentions, there should be no problem in getting the antennas to low enough power.  Keep in mind, however, that a standard antenna will not give single photon output statistics.

In addition to @Enrico's links, I found this rather good reference on detectors:

Susumu Komiyama, Single-Photon Detectors in the Terahertz Range, IEEE JOURNAL OF SELECTED TOPICS IN QUANTUM ELECTRONICS, VOL. 17, NO. 1, Page 54, JANUARY/FEBRUARY 2011

It seems harder to find publications on true THz single photon sources, although I'd guess you could probably do it with quantum dot/SET type structures.

What Marek describes is inelastic photon scattering such as in the Compton effect. This is actually a nice piece of physics to consider, since the kinematics, as Marek says, is correctly described by a "particle billard" like, quasi-mechanic description, while the change of energy of the photon is actually detected as a change of wavelength evidenced by a monochromator (\lambda *E / \hbar = c). [In an adequate theoretical framework, this would actually rather be described as the destruction of the original photon and the creation of a new one with different energy and momentum, rather than a change of the properties of some specific photon.]

As was said before, in the photoelectric effect, the elementary process is photon absorption, i.e. the photon is being destroyed in the process, and its energy (and momentum) is being taken up by "the system" in such a way that the end product comprises an electron escaping from the absorbing atom (or solid).

As I understand the original question, the inquiry is about the details in time (evolution) of this process. One usual attempt to do this is to use so-called time dependent perturbation theory, where the perturbation is assumed to be an electromagnetic field, for example in the shape of a plane wave of given frequency. This is a so-called semi-classical approach to the problem, since the electomagnetic field is modeled as a classical field sufficiently weak to not perturb the quantum states of "the system". Carrying out this calculation leads indeed to a time evolution of the quantum system, resulting in an oscillation between the two quantum levels being coupled by the radiation field (Rabi-oscillations). However, one inherently assumes in this approximation that the e/m field itself is unchanged, so that the detailed energy conservation issues are not properly treated. Nevertheless, the approach is useful for many computations (transition matrix elements are correctly computed in this approximation, the absorption probabilities derived from them "survive" the transition to the fully quantum description).

The time evolution thus computed derives from the explicit time dependence of the classical electromagnetic field. The quantum nature of radiation is not included here (so there are no photons in this description). Photons, in turn, are to be understood as quantized modes of the electromagnetic field. It is an inherent property of single photon states that we cannot attribute classical field properties like E(r,t) to these states. The expectation values of the classical field quantities E and H actually vanish at all r and t (in other words: the phase of the e/m field in a single photon state is not determined. Messiah's books on QM would probably be a suitable place to look this up). As I understand it, the time evolution of the absorption (annihilation) of a single photon therefore concerns a question that cannot be answered in the full quantum description (the framework for this would be quantum electrodynamics). This is not dissimilar to the case of radioactive decay, where we know the probability for something to happen, but not the moment in time when a particular individual decay will occur.

QM states of the e/m field with known/defined phase (i.e. coherent radiation) can nevertheless be constructed, they are referred to as Glauber states. The price to pay for this information is that the number of photons is actually unknown (this is yet another version of the Heisenberg uncertainty principle), because to obtain such states one needs to superimpose states with 1,2,3,..,n,... photons. This means that the energy of the e/m field in such a state is indetermined...  Lasers produce an approximation to such coherent e/m fields. Therefore, using such coherent light sources one can nevertheless observe Rabi-oscillations (in sufficiently simple systems).

This answer has neither been short, nor particularly simple, sorry. Hope it nevertheless helps as an orientation. (And of course, it only reflects my understanding of the subject...)

Note added: To come back to the original formulation of the question and to reinforce a statement made earlier in this thread, the formulation "removal of photons from electrons" is not adequate. Rather, e.g. in considering the process of photon absorption by a hydrogen atom, we would have to view the entire system of matter (proton & electron) and the electromagnetic field as one system. In modeling it, we first describe them separately (e.g. by computing all the stationary solutions of the Hydrogen atom problem on the one hand, and the quantized modes of the e/m radiation field on the other, described as continua of e/m harmonic oscillators). The basis states in this description would just be product states of atomic excitations and e/m excitations (photons), and these states would be stationary (i.e. 'live' forever). Next we introduce the coupling between the two (it must be finite, otherwise there could be no interaction/absorption). In principle, we would now have to solve the coupled system (as a result the original basis states are no more stationary). If the coupling is weak enough it is permissible and a very good approximation indeed to continue using the product states as the basis of the language in which we describe the processes. There remains the problem of photon creation out of an excited state, which was also mentioned in the original question. The initial state would consist of "excited atomic state" * "no photon". Now with (apparently) no electromagnetic field, how can a photon be created? The fascinating answer is that the state "no photon" is actually not equivalent with "no e/m field. The rates/probabilities of this "sponataneous" emission are adequately described by considering the zero point fluctuations of the electromagnetic field" (related to the fact that QM harmonic oscillators in their lowest energy state have nonzero energy). 

I think that a significant amount of the physics will be similar to what has been seen in N type systems (again 4 level and 3 fields), although of course the emission properties will be different due to the three excited states (as you mention).  If some of the fields are degenerate, (for example you look for two-photon transitions mediated by a central state), then you should get some physics that is like diamond type systems (ladder with two quasi-degenerate middle states).

David McGloin had an excellent article on what I believe is the same system from 2003 - 

Coherent effects in a driven Vee scheme

D McGloin - Journal of Physics B, 36 (2003) 2861–2871.

I would humbly suggest that my NJP paper on quantum nonlinear processes in the N system might also give you some good references

Single photon quantum non-demolition measurements in the presence of inhomogeneous broadening, Andrew D Greentree, R G Beausoleil, L C L Hollenberg, W J Munro, Kae Nemoto, S Prawer and T P Spiller, New Journal of Physics 11, 093005 (2009).

Hope this helps

Just to bring some additional noise into an already complex issue. Let me first state that over all, I agree with Gert. However, are not other scenarios possible? Thus, we know (Mössbauer effect) that emission of a photon can transmit the recoil momentum on the center-of-mass of the emitting crystal. And, of course, the inverse process, in which the photon transfers its whole momentum to the crystal as a whole, is also possible.

So, under ordinary circumstances, I have no argument that the likeliest process by far is conversion to microscopic motion. But other stuff can happen.

Dear Derek,

I assume you know about ESA's recently approved Explorer mission 'FLEX', but if not, you'll find more information about it here:

Of course, a web search for "esa explorer fluorescence" will generate thousands of pages... Now, plant materials are quite different from an acrylic plastic sheet, but perhaps some of the physics may be relevant.

Good luck with your investigation. Cheers, Michel.

I suggest looking in Part III, Complement 7A of G. Greenberg, A. Aspect, C. Fabre "Introduction To Quantum Optics". The book discusses why PDC can be explained both quantum mechanically and semiclassically but SPDC - only quantum mechanically.

Hi,

If you're only interested in finding the angles so you could order crystals from a crystal supplier, the easiest way is to use SNLO software: http://www.as-photonics.com/snlo

If you're also intersted in searching for the exact phase-matching angles yourself, first you should decide whether you're interested in a collinear solution, in which the pump photon and the two down-converted photons propagate in the same direction, or a non-collinear solution, in which the directions of the pump differs from the direction of the down-converted photons (this naturally coplicates the calculation). Then, you should decide if you're interested in a degenerated case, in which the down-converted photons share the same wavelength, or not.

Then, search for the crystal's Sellmeier's equations, which relate the wavelength to the refractive index (note that there are two equations for uniaxial crystals, one for the ordinary and the other for the extraordinary polarizations). After deciding on the specific wavelengths you're intersted in, calculate no and ne for the wavelengths involved in the process using the Sellmeir equations. All you have to do now is use a computer program to solve the energy and momentum equations for the three photons invloved in the process, depending on the specific process you've chosen (collinear/non-collinear, degenerated/non-degenerated, etc.) . 

For that you should choose an input polarization and define a propagation direction within the crystal. For a uniaxial crystal, only a single angle (usually referred to as theta) is enough. Using this angle you could find the two refractive indices eigenmodes [no, ne(theta)], and use them to solve the momentum conservation equation.

More details (regarding a more general case in which the crystal is biaxial) can be found at:

A. Halevy, E. Megidish, L. Dovrat, H.S. Eisenberg, P. Becker, and L. Bohatý, “The biaxial nonlinear crystal BiB3O6 as a polarization entangled photon source using non-collinear type-II parametric down-conversion,” Opt. Express 19, 20420–20434 (2011).

Another very relevant article is the following:

N. Boeuf, D. Branning, I. Chaperot, E. Dauler, S. Guérin, G. Jaeger, A. Muller, and A. Migdall, “Calculating characteristics of noncollinear phase matching in uniaxial and biaxial crystals,” Opt. Eng. 39, 1016–1024 (2000).

I hope it helps,

Assaf

The D86 is also called encircled energy (but is in fact encircled intensity that is measured and energy is computed), this is generally the way that all short-pulse laser systems measure the intensity on target. This is the technique used in my post above to calculated the spot size from a CCD as you need some point of reference to know where to stop your contour, and this number can be essentially arbitrary because the spot may deviate significantly from Gaussian. Also, this number can be manipulated to make your laser look better than it is, i.e. taking the 50% contour instead of the 86% contour can yield a much higher average intensity, thus as a best practice one should not quote a number, but rather show the encircled energy curve. See attached Fig 2, encircled energy at best focus, and attached image of the focal spot through focus.

Actually in a quantum field theory A_μ field has four components. But physically it should have only two components, which are transverse to the direction of motion. These are polarization states. A₀ is determined by specifying the three vector A. In Coulomb gauge additional constraint on A_μ is ∇.A=0, this in turn fixes A₀=0. We see that this is a constrained system. Quantization of a constrained system can be found  for example in "Lectures in quantum mechanics" by P. A. M. Dirac.

I understand that they are different. In fact Smith Purcell effect is an example of Cherenkov radiation ; instead of slowing light by entering a medium with high refractive index due to the polarization of its molecules, light propagates by exciting another dipole and its phase velocity is now slower just because gratings reduce the phase velocity of light. What i am really wondering about is whether the electron parallel to grating rulings imparts a tangential momentum on the metal (which is a standard way to excite SPP) and then the gratings out couple it to the far field as light . 

From a process, procedural standpoint, three level systems, provide an avenue for transitions instead of a truncated, two-level, start to finish, beginning to end. While three is more realistic, two may be more amendable to binary logic and hence computable approaches.

Thank you Professor. I have just sent the other books into your inbox. Yes you are right, I have been having challenges with how to place  the integration variable τ. The problem I wish to apply the solution to would be meaningless if the integral has infinite upper limit; it has to be finite. I have already obtained analytical function for the expectation value (which can be easily differentiated or integrated as the situation requires); the challenge (which concerns the evaluation of any existing commutation relations; as shown in Principles of nuclear magnetism by A. Abragam, 1961, page 23) now is how to handle the right hand side of equation (6) in order to obtain f(x) in terms of the analytical function. I am really sorry if I am not asking the right questions!

Yes, of course there is: cyclically birefringent crystals for example.

When the axis of polarization is changing while passing through the crystal it is precisely this what is happening.

Polarisation is an internal degree of freedom, like the z-component of a spin for example. An electron may also have different components in its wave funtion, but it cannot be split (at least not following nowadays knowledge).

In the same way one must see the photon: it may have different internal degrees of freedom, but you cannot split it into two "halves". I think, QED is old enough for being checked to the details, and polarisation is NOT a detail; it's essential.

You could of course use this internal degree of freedom to create entangled states in two photons...(hyper-entanglement)