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# Bose-Einstein Condensates - Science topic

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Questions related to Bose-Einstein Condensates

1. Bose-Einstein condensation: How do we rigorously prove the existence of Bose-Einstein condensates for general interacting systems? (Schlein, Benjamin. "Graduate Seminar on Partial Differential Equations in the Sciences – Energy, and Dynamics of Boson Systems". Hausdorff Center for Mathematics. Retrieved 23 April 2012.)

2. Scharnhorst effect: Can light signals travel slightly faster than c between two closely spaced conducting plates, exploiting the Casimir effect?(Barton, G.; Scharnhorst, K. (1993). "QED between parallel mirrors: light signals faster than c, or amplified by the vacuum". Journal of Physics A. 26 (8): 2037.)

Hello, someone could provide me your code to analyze it, investigating I have seen that the Gross-Pitaevskii equation is solved for simulation, is there any other simpler way or in any case what would be the simplest case to perform the simulation for the Gross-Pitaevskii equation?

Dear colleagues, what do you think of a possible mathematical analogy between a one-sided surface and a Bose-Einstein condensate?

in trying to undestad conformal field theory with holography,probably i need help bacause ¿how ads/cft can have implications in experimental areas?

Could quasi-periodic tilings play a part in High temperature Superconductivity ? Even in a heated disordered state, could the quasi-crystalline nature of the material enforce some kind of order wherein the global and local properties are interconnected ? Breaking this could possibly require very large amount of energy which could lead to a cooling of the system which could make the system amenable to the influence of electromagnetic fields which could lead to a disorder - order transition (associated with many phenomenon such as Bose Einstein Condensation, Superfluidity, Superconductivity etc) with associated dissipation of energy and further cooling.

Could the above play a part in diffractive rsdiative processes dominating over conductive diffusive processes ?? (Possibly through smooth but non-differentiable solutions of the associated transport equations due to singularities at multiple scales which could lead to localization). Could this be a mechanism for inducing superconductivity ? Could such fields / modes induce waveguides for photons / electrons / phonons and their bound states , especially through solitons etc ? And could this be related to superconductivity ??

The occupation number of bosons can be any number from zero to infinity, guiding us to the Bose-Einstein statistics. On the other hand, for example, a classical wave can be considered a superposition of any number of sine or cosine waves. Isn't it similar to say the occupation number of a classical wave can be any number from zero to infinity and utilizing Bose-Einstein statistics for classical waves in particular and classical fields in general?

Rogue waves are an important topic in water waves, plasma physics, nonlinear optics, Bose Einstein condensate and so on

How can we predict a rogue wave?

Many thinkers reject the idea that large scale persistent coherence can exist in the brain because it is too warm, wet, noisy and constantly interacts, and consequently, is 'measured' by the environment via the senses.

The problem of decoherence is, I suggest, in part at least, a problem of perception - the cognitive stance that we adopt toward the problem. If we examine the problem of interaction with the environment, common sense suggests that we perceive the primary utility of this interaction as being the survival of the organism within its environment. It seems to follow that if coherence is involved in the senses then evolution must have found a way of preserving this quantum state in order to preserve its functional utility - a difficult problem to solve!

I believe that this is wrong! I believe that the primary 'utility' of cognition is that it enables large scale coherent states to emerge and to persist. In other words, I believe that we are perceiving the problem in the wrong way. Instead of asking 'How do large scale coherent states exist and persist given the constant interaction with the environment?', we should ask instead - 'How is cognition instrumental in promoting large scale robust quantum states?'

I think the key to this question lies in appreciating that cognition is NOT a reactive process - it is a pre-emptive process!

As you know I had proposed

Achimowicz formulae stating that Information can be transformed to energy by the relation:
(1) E = I x c2
in analogy to reasoning that
E= m x c2 = h x omega as proposed by Planck

*The next step is quantomize information so I shoud write:*

*E= I x c2 = h x omega*

*where h - Planck constant and omega is the information frequency.* Next question is : Does DNA have the own frequencies i.e. stable information frequencies at which it resonates?

. So what the quanta of information means ????

What is its interpretation ???

Any one wishing to answer this question ???

Collective effects are evident in billions and billions of particles or entities in physics, such as In lasers, electromagnetism [1], superconductivity, critical mass in nuclear physics, physics of fluids, thixotropic and other non-newtonian effects, fusion and fission, binding energy, gravity, and quantum mechanics.

There are applications also in maths. We discussed its application in social movements, where statistics is not used, nor psychology, but a causal model is introduced, based on physics of fluids and collective effects.

The problem is that a system made of billions of billions of particles or entities, as usual in physics of natural systems, is much harder to study, for example, in quantum behaviour or even classical.

In network theory, comes the example of 6 degrees of separation. Now, in physics [2,3], comes the example of 10 photons. Studying quantum behaviour of particles is much easier with fewer particles, so the fact that phase transitions occur in these small systems means we can better study quantum properties such as coherence.

Could we start to see behaviour of collective effects with 10 electrons or less? Can we use them to better study coherence also in non-quantum behaviour? What is the lower limit?

[1] Carver Mead, Collective Electrodynamics: Quantum Foundations of Electromagnetism,

[3] Driven-dissipative non-equilibrium Bose–Einstein condensation of less than ten photons, https://www.nature.com/articles/s41567-018-0270-1

All the research papers I found so far, are just showing measurement of the squeezing parameter or quantum Fisher Information (QFI). Of course authors mention that, due to large QFI or strong squeezing this setup can be used for metrological purposes beyond standard quantum limit (SQL). I could not find any papers, which actually perform estimation of the

**unknown**phase and show that the precision is beyond SQL. I am curious from the point of view of estimation in the presence of decoherence (which is always present). Theoretical papers indicate that entangled states are basically useless if frequency is estimated (e.q. Ramsey spectroscopy).Many nonlinear equations are solved for soliton solutions using Hirota bilinearization method but those equations are proven to be integrable either in inverse scattering sense or Lax pair method. Is it correct to use the Hirota bilinearization for nonintegrable systems?

If its possible to create a Bose-Einstein condensate for which no possible Fermi interactions can prevent further collapse and the mass was large enough, could the system collapse into a black hole? For integer spin particles might this be not only for baryons, but also for photons, since they have effective mass and are acted on by gravity? This might be if intensity of photon beam, ie energy density were large enough, perhaps even if the beam were slowed down in a condensate, to increase the energy density.

I am interested in coupling between collective modes of a BEC. Is there any experiment observing several collective modes simultaneously, and, l=0 mode with other modes?

I would like to know if the energy gap between ground state and the first excited state in a Bose-Hubbard model have been determined? In particular I would like to know how does it scale with the system size? So far I couldn't find any numerical data for 1D, 2D or 3D.

https://en.wikipedia.org/wiki/Superfluidity: Superfluidity is the characteristic property of a fluid with zero viscosity which therefore flows without loss of kinetic energy. When stirred, a superfluid forms cellular vortices that continue to rotate indefinitely. Superfluidity occurs in two isotopes of helium (helium-3 and helium-4) when they are liquified by cooling to cryogenic temperatures. It is also a property of various other exotic states of matter theorized to exist in astrophysics, high-energy physics, and theories of quantum gravity The phenomenon is related to Bose–Einstein condensation, but neither is a specific type of the other: not all Bose-Einstein condensates can be regarded as superfluids, and not all superfluids are Bose–Einstein condensates

Can any one suggest me best articles for quantum simulations of ultracold quantum gases

Hello all,

I have started reading about diffractive optics. The papers and books I have read till now, all claim that

"It is extremely difficult (impossible?) to find closed-form diffraction solutions

using the Rayleigh–Sommerfeld expression for most apertures. The Fresnel

expression is more tractable, but solutions are still complicated even for simple cases such as a rectangular aperture illuminated by a plane wave."

I want to know why does this happen?

Dear Colleagues,

In automatized quantum chemical calculations (such as Chem Bio 3D Ultra) sometimes the IR/Raman spectra are not generated due to the fact that out of the first 6 frequencies (which obviously belong to the translation and rotation degrees of freedom) one is negative. This happened in relatively simple, symmetric structures, including ring compounds, after performing geometry optimization. I am fully aware of the fact that in saddle point geometries there may happen negative frequency, but I would not expect it in stable ring structures. I would like to know what is the reason (I am sure it is a kind of artifact) and, most importantly, how can it be avoided. Apparently the problem is only that the simulated spectrum is not plotted, otherwise the rest of the frequencies seem to be reasonable.

Dear Friends,

I want to get the article which clearly illustrate how the atomic s-wave scattering length in Bose-Einstein Condensates (BEC) can be tuned spatially by means of external magnetic and/or optical trapping fields. Please let me know the references. Thanks in advance.

With warm regards

jbSudhan

Fröhlich proposed that when proteins absorb a terahertz photon the added energy forces the oscillating molecules into a single, lowest-frequency mode which supports the Orch-OR theory of consciousness by Hameroff and Penrose. In contrast, other models predict that the protein will quickly dissipate the energy from the photon in the form of heat. This was challenged by Reimers and group in 2009, where the group demonstrated that no amount of mechanical energy can produce a coherent Fröhlich condensate. But in a recent 2015 study, Katona and his colleagues concluded that the long-lasting structural changes that were observed in the helical structure of the lysosome crystal could only be explained by Fröhlich condensation, a quantum-like collective state in which the molecules in a protein behave as one.

Recently I was interested in the Efimov effect. I read some reference of related experimental research. I found all these experiments used ultra_cold atoms but not Bose-Einstein condensates(BECs) although all these group are able to creat BECs. So I want to know why people did not use BECs in this kind experiment?

Dose it due to the high density or the many-body correlation of BECs?

In dealing with Bose-Einstein statistics, assuming that the ground state energy is zero, it is concluded that the chemical potential of Bose gas system must be negative. How can we explain the zero energy ground state and its meaning?

Hi all,

This is a pure curiosity question. Obviously, Superfluid helium has to do with BECs (in particular, it is implicitly suggested by Feynman in his famous lectures). However, my idea of a BEC is that it is like a Maser, or a matter Laser, right ? So in principle, all the bosons in the BEC have the same QM state vector, don't they ? But in superfluid helium, we can see a thin film climbing up and down the walls of the beaker, which shows that at least some particles don't have the same momentum as everyone else in the beaker. So is superfluid helium really a BEC ? And if not, is it because it is in a quite dense state, whereas most BECs are obtained in a low density gaseous state ?

To obtain some nonlinear equation from physical models we use the stretched variables in a very limited approximation.

For example, to obtain KdV equation which is a nonlinear equation with weak dispesrions and weak nonlinearities. We use the transformation X and T with n=1/2.

I want to know more about this stretched variables and their domain of validity.

See Links Below for

Gravational Waves, Bose Einstein Condensate, Magnetic-Optic Traps. Ion Traps and Far Off Resonance Traps.

What are the experimental methods to find quasiprobability distributions/density matrix of a two-mode Bose-Einstein condensate.

All that I have about the Bose-Einstein distribution is the statistics of the occupation number

*n*of the*j*-th energy level,(1) <

*n*> = 1/{exp[(_{j}*μ*-_{j}*ϵ*)/_{j}*k*_{B}*T*] - 1}where

*μ*is the chemical potential on the_{j}*j*-th level, and*ϵ*the level energy. However, I would like to calculate the average kinetic energy in the gas, i.e._{j}∑

_{j }nj*E*_{kinetic},*/∑*_{j }*, also the most probable kinetic energy in the gas, and the similar quantities for velocity.*_{j}n_{j}Does somebody know a simple way to do it?

It has been a popular belief that super fluidity of He-II and of trapped dilute Bose gases arises due to macroscopically large fraction of particles in a single particle state of momentum p=0. It appears that the number of He atoms in He-II in such state is as low as 10% as concluded presumably by theory and experiment. However, if 10% He-atoms in p=0 state can produce super fluidity, then 1% can also do and if 1% can do so, 0.1% can also do and so on ...., unless there is a minimum bound by some law of nature. It is natural therefore to know the law which decides this lower bound and what is the value of the lower bound number of He-atoms in p=0 state which can produce super fluidity ?.

It is known that bosons have a bunching tendency. Assume that the bosons are atoms of a gas in a magnetic trap. At high temperatures this effect is not obvious. But, if we decrease the temperature (though keeping it above the temperature of transition to BEC), what I see in reports is that the bunching tendency increases.

Why does this happen? It seems to me that the bunching effect should become less and less obvious as we get closer to the transition temperature. Due to the increase in density the atoms get anyway closer to one another, and on the other hand, there is electric repulsion between the electron clouds of the atoms. So, the bunching should become less visible.

Whatever I can say about lowering the temperature, is that the average linear momentum of the atoms decreases and the inter-atomic distance decreases, s.t. the average distance between the atoms in the position-momentum phase-space decreases.

But bunching is a two-particle interferometry effect. I don't see the connection with the distance in the phase-space. To the contrary, as the temperature decreases and the density in the ordinary space increases, it seems to me that it would be more difficult to distinguish between a pair of atoms close to one another because of the increased density, and a pair of atoms close because of the bunching.

Where am I wrong?

In the recent Australian National University experiment by Dr. Truscott, Wheeler's Delayed Choice thought experiment was carried out with ultra-cooled helium atoms. The Nature Physics publication is below, with other explanations available online. What I'm interested in is a plausible explanation that occurred to me.

So, the state of the atom is indeterminate between the first light grating and the second possible light grating. This second event, only determined to actually happen (or not) after the first event occurs, seems to influence the behavior (either particle or wave behavior) of the atom between the first and second grating. There are two plausible explanations. Either the atom doesn't actually exist as a wave or particle between these two events, and this behavior is only determined at measurement, or (obviously controversially) the future event effects the past.

I'm interested in this second explanation, because in my mind it resembles the local-realism violations of certain entangled pairs. There is support to the idea that a particle can be entangled with itself (though the usefulness of this until now was moot), so my question, as stated above, is this: could this single helium atom be entangled with itself between the first and second gratings? As a measurement of one entangled particle causes the other to take on the measured state, this behavior seems at the very least parallel. When this atom is measured at the second grating (let's call this t=1), not only is the behavior determined for that point, but as that collapses the superposition of having traveled as either a wave or particle, it also collapses it at its state immediately after the first grating (for now, t=0).

This does require the atom as it exists at t=0 and at t=1 to be considered an entangled pair to have a consistent explanation, hence the question.

We need to wind a pair of anti-Helmholtz coils and we would like to use wire that has a rectangular cross section to maximize the filling ratio.

Can anyone recommend a company that sells something usable (not to thick) and reasonably priced?

Any suggestion or discussion about the question

Does anyone have experience with this system, and, if so, what is the minimum achievable linewidth?

Furthermore, do you know some problems that would lead to linewidth broadening and how to solve them?

In BEC no. of atoms should remain constant. That's why we can not use same statistics for photon. but,

1)what are the

**?, which will show BEC.***minimum no of atoms*2)What about

**(BEC) and why?***one atom*3) Can we somehow use such condensation for

**?***Photons*BEC represents order in momentum space, which is fictitious. It occurs at k = 0 (or, more precisely, at the lowest momentum state, depending on the observer's reference frame). This corresponds to the infinite- (or large-) r limit in configuration space. How exactly? How does no (the condenate fraction) appear in this space (which is related to momentum space through, of course, a Fourier transform)?

There exists a vast literature on superfluidity. It is growing daily, now that we are drawn more and more to low-dimensional systems, both theoretically and experimentally. One thing is clear: superfluidity and Bose-Einstein condensation are two distinct phenomena, the one not necessarly implying the other. I sympathize with beginners in the field; there is so much confusion, although the phenomenon is now a few years older than a century!

Solitons are the 1D topological defect with phase singularity of \pi, whereas vortices have \2pi phase jump around its core. Recently the obsevation of solitonic vortex in BEC has been confirmed. Can anybody elaborate solitonic vortex clearly?

Klein-Gordon relativistic equation (although not a fancy of a majority) with addition of magnetic vector potential will also give rise to GPE equation. So, whatever be the route, the BEC formation should be judged by number density and temperature as well as effective mass that should be large for condensation. This is again related to temperature and scattering-length parameter.

When we are dealing with a system of small or large number of interacting bosons confined in a potential, what are the parameters which provides information about the Bose-Einstein condensation and condensate fractions?

The dynamics of BEC trapped in optical lattice is governed by the discrete nonlinear Schrodinger equation (DNLSE). In tight binding limit, one can expand the condensate order parameter in terms of Wannier basis function. This basis function is further used in the calculation of the tunneling energy (J), offset energy (V_n) and interatomic interaction strength (U). Is there a way to calculate the Wannier basis numerically?

I am trying to understand the nature of Bose-Einstein Condensates and the possibility that they may be associated with living processes. My intuition tells me that they must be scale -free processes. Can anyone confirm this intuition with some references?

I am no physicist, but I am a writer and a fan of SF. The Bose-Einstein Condensate is surely one of the most fascinating 'artifacts' to be produced in recent years and may have significance in as wide-ranging fields of enquiry as consciousness to safe energy.

I want to write (or rather complete) a novel that explores these possibilities, but I want to stray as little as possible from current theoretical models, whilst indulging myself and the reader with some of the fantastical explorations true to the spirit of SF.

Can anyone help me? A sufficiently great contribution will entitle my collaborator to acknowledgement, if not the title of co-author.

I have started a Project [The Bose-Einstein Condensate (A Novel] and one Bench [Drafts]

How the von-Neumann entropy (quantum entropy) and "quantum correlations" related to each other for a system of cold atoms? Is there any other parameter to measure the quantum correlations between the atoms?

The minimum temperature of trapped ions corresponds to the ground state of the trapping potential. Thus, in principle, the ions are cooled down to lower temperature as the frequency of the trapping potential is reduced. Where does the limitation come from?

For imaging of nanoscale objects, optical microscopy has limited resolution since the objects are often much smaller than the wavelength of light. One can achieve a considerable improvement in resolution with instruments such as the transmission electron microscope and the scanning electron microscope that use electrons with De Broglie wavelength much smaller than that of visible light. To image picoscale and maybe attoscale objects, in principle, we may need a coherent beam of atoms because it may have a smaller De Broglie wavelength than that of electron beam!

First principle wave mechanical formulations reveal that a quantum particle in any potential trap has non-zero energy in its ground state. This implies that no atom of trapped dilute boson gas in a harmonic potential trap used to achieve its BEC state can have zero energy/momentum. However, people in the field claim that a macroscopically large number of atoms (say about 60% just for an example) in the lowest temperature BEC state achieved by them have zero momentum. Can any body kindly help me understand the reality? This is a state of great confusion.

What are the advantages of CPD over the usual single particle density?

Could we say that the reason of wavy behavior of the atoms in zero temperature in BEC is the minimum entropy (minimum distortion for creating solitons)?

I'm using 'ListDensityPlot[]' from MATHEMATICA to do contour plot. But it seems too slow and the fiures taking large memory. Actually, I'm generating the datas using C and stored in external file in '.dat' (file size is about 10-20 MB)format. But I like to do the Contour plot using Python.

Note that theoretically the existence of this wave in BEC has been demonstrated .

When condensate is loaded in optical lattices, non-linearity (atom-atom interaction) play a vital role in the diffusion dynamics. For some critical value of non-linearity of the condensate, diffusion is suppressed and it is said that the system is in self-trapped state. This suppression of diffusion is due to steep edges developed on both side of condensate(in 1D lattice case). But after some time these steep edges dissolve and diffusion restarts, there comes another critical time where the diffusion suppressed again and so on. I am searching a review article on self-trapping of condensate in optical lattice potentials 1D, 2D and 3D.

When vortices in BEC annihilate then they dissipate their energy in the form of a sound wave. Is there any theoretical way to calculate that sound energy?

Condensate trapped with weak optical lattice confinement in one direction and stronger one in other two form a quasi-one dimensional condensate. What is the life time observed for 1-d condensate to the date?

Of course, the answer depends on the chosen measurement technique -- anyway I am curious especially in the case of so-called fragmented Bose-Einstein condensates or Tonks-Girardeau gases.

By one-body density, I mean the diagonal of the reduced one-body density -- that is obtained by tracing out all but one coordinate from the wavefunction multiplied with its complex conjugate.

By many-body or N-body density, I mean the diagonal of the N-body density -- that is obtained as the wavefunction multiplied with its complex conjugate.

From a physical point of view it would be very interesting to find a way/technique to distinguish the cases where the N-body is not just a product of one-body densities from the cases where it is such a product. I know, there is interference experiments, but a way relying on just imaging would be more easily managable.

Cooling quantum gasses leads to Bose-Einstein condensation and there are limitations in each cooling technique. Different schemes are applied to achieve condensate with temperature in the range of Micro Kalvin. I just want to know the reference which can tell me the lowest temperature achieved.

Is there is any harmonic trapping potential in Bose-Einstein Condensates in the form of v(x,t)=lambda(x,t)^2(x^2/2) ie., the lambda is varying with both space (x) and time (t). Can anyone suggest any references about this?