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ABSTRACT: This paper shows that phase space methods using a positive P type
distribution function involving both c-number variables (for the cavity mode)
and Grassmann variables (for the two level atom) can be used to treat the
Jaynes-Cummings model. Although it is a Grassmann function, the distribution
function is equivalent to six c-number functions of the two bosonic variables.
Experimental quantities are given as bosonic phase space integrals involving
the six functions. A Fokker-Planck equation involving both left and right
Grassmann differentiation can be obtained for the distribution function, and is
equivalent to six coupled equations for the six c-number functions.
The approach used involves choosing the canonical form of the (non-unique)
positive P distribution function, where the correspondence rules for bosonic
operators are non-standard and hence the Fokker-Planck equation is also
unusual. Initial conditions, such as for initially uncorrelated states, are
used to determine the initial distribution function. Transformations to new
bosonic variables rotating at the cavity frequency enables the six coupled
equations for the new c-number functions (also equivalent to the canonical
Grassmann distribution function) to be solved analytically, based on an ansatz
from a 1980 paper by Stenholm. It is then shown that the distribution function
is the same as that determined from the well-known solution based on coupled
equations for state vector amplitudes of atomic and n-photon product states.
The treatment of the simple two fermion mode Jaynes-Cummings model is a
useful test case for the future development of phase space Grassmann
distribution functional methods for multi-mode fermionic applications in
quantum-atom optics.
03/2012;
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ABSTRACT: A key goal of quantum communication is to determine the maximum number of
bits shared between two quantum systems. An important example of this is in
entanglement based quantum key distribution (QKD) schemes. A realistic
treatment of this general communication problem must take account of the
nonideal nature of the entanglement source and the detectors. The aim of this
paper is to give such a treatment. We obtain analytic expression for the mutual
information in terms of experimental parameters. The results are applied to
communication schemes that rely on spontaneous parametric down conversion to
generate entangled photons. We show that our results can be applied to tasks
such as calculating the optimal rate of bits per photon in high dimensional
time bin encoded QKD protocols (prior to privacy amplification). A key finding
for such protocols is that by using realistic experimental parameters, one can
obtain over 10 bits per photon. We also show how our results can be applied to
characterize the capacity of a fibre array and to quantify entanglement using
mutual information.
03/2012;
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ABSTRACT: This paper presents the general Schmidt decomposition of two-photon fields
generated in spontaneous parametric down-conversion (SPDC). It discusses in
particular the separation of the radial and azimuthal degrees of freedom, the
role of projection in modal analysis, and the benefits of collinear phase
mismatch. The paper is written in a review style and presents a wealth of
numerical results. It aims at emphasising the physics beyond the mathematics,
through discussions and graphical representations of key results.
01/2012;
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ABSTRACT: The Thomas-Reiche-Kuhn sum rule is a fundamental consequence of the position-momentum commutation relation for an atomic electron and it provides an important constraint on the transition matrix elements for an atom. Analogously, the commutation relations for the electromagnetic field operators in a magnetodielectric medium constrain the properties of the dispersion relations for the medium through four sum rules for the allowed phase and group velocities for polaritons propagating through the medium. These rules apply to all bulk media including the metamaterials designed to provide negative refractive indices. An immediate consequence of this is that it is not possible to construct a medium in which all the polariton modes for a given wavelength lie in the negative-index region.
Physical Review Letters 01/2012; 108(1):013601. · 7.37 Impact Factor
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ABSTRACT: We examine how to distinguish between unitary operators, when the exact form
of the possible operators is not known. Instead we are supplied with "programs"
in the form of unitary transforms, which can be used as references for
identifying the unknown unitary transform. All unitary transforms should be
used as few times as possible. This situation is analoguous to programmable
state discrimination. One difference, however, is that the quantum state to
which we apply the unitary transforms may be entangled, leading to a richer
variety of possible strategies. By suitable selection of an input state and
generalized measurement of the output state, both unambiguous and minimum-error
discrimination can be achieved. Pairwise comparison of operators, comparing
each transform to be identified with a program transform, is often a useful
strategy. There are, however, situations in which more complicated strategies
perform better. This is the case especially when the number of allowed
applications of program operations is different from the number of the
transforms to be identified.
09/2011;
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ABSTRACT: We consider the possibility of performing quantum key distribution (QKD) by encoding information onto individual photons using plane-wave basis states. We compare the results of this calculation to those obtained by earlier workers, who considered encoding using OAM-carrying vortex modes of the field. We find theoretically that plane-wave encoding is less strongly influenced by atmospheric turbulence than is OAM encoding, with potentially important implications for free-space quantum key distribution.
Optics Express 09/2011; 19(19):18310-7. · 3.59 Impact Factor
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ABSTRACT: Spontaneous parametric down-conversion has been shown to be a reliable source of entangled photons. Among the wide range of properties shown to be entangled, it is the orbital angular momentum that is the focus of our study. We investigate, in particular, the bi-photon state generated using a Gaussian pump beam. We derive an expression for the simultaneous correlations in the orbital angular momentum, ℓ, and radial momentum, p, of the down-converted Laguerre-Gaussian beams. Our result allows us, for example, to calculate the spiral bandwidth with no restriction on the geometry of the beams: ℓ, p, and the beam widths are all free parameters. Moreover, we show that, with the usual paraxial and collinear approximations, a fully analytic expression for the correlations can be derived.
Phys. Rev. A. 03/2011; 83(3).
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ABSTRACT: We examine the physical implementation of a discrete time quantum walk with a
four-dimensional coin. Our quantum walker is a photon moving repeatedly through
a time delay loop, with time being our position space. The quantum coin is
implemented using the internal states of the photon: the polarization and two
of the orbital angular momentum states. We demonstrate how to implement this
physically and what components would be needed. We then illustrate some of the
results that could be obtained by performing the experiment.
03/2011;
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ABSTRACT: We examine the implementation of an arbitrary U(4) gate consisting of CNOT gates and single qubit unitary gates for the Hilbert space of photon spin polarization and two states of photon orbital angular momentum. Our scheme improves over a recently proposed one that uses q-plates because the fidelity is limited only by losses thus in principle it could be used to achieve a perfect transformation. Comment: 7 pages, 1 figure
12/2010;
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ABSTRACT: Entanglement of the properties of two separated particles constitutes a fundamental signature of quantum mechanics and is a key resource for quantum information science. We demonstrate strong Einstein, Podolsky, and Rosen correlations between the angular position and orbital angular momentum of two photons created by the nonlinear optical process of spontaneous parametric down-conversion. The discrete nature of orbital angular momentum and the continuous but periodic nature of angular position give rise to a special sort of entanglement between these two variables. The resulting correlations are found to be an order of magnitude stronger than those allowed by the uncertainty principle for independent (nonentangled) particles. Our results suggest that angular position and orbital angular momentum may find important applications in quantum information science.
Science 08/2010; 329(5992):662-5. · 31.20 Impact Factor
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ABSTRACT: We investigate multi-boson interference. A Hamiltonian is presented that treats pairs of bosons as a single composite boson. This Hamiltonian allows two pairs of bosons to interact as if they were two single composite bosons. We show that this leads to the composite bosons exhibiting novel interference effects such as Hong-Ou-Mandel interference. We then investigate generalizations of the formalism to the case of interference between two general composite bosons. Finally, we show how one can realize interference between composite bosons in the two atom Dicke model.
03/2010;
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ABSTRACT: It is 100 years since Minkowski and Abraham first gave rival expressions for the momentum of light in a material medium. At the single-photon level, these correspond, respectively, either to multiplying or dividing the free-space value (symbol:see text) by the refractive index (n). The debate that this work started has continued till the present day, punctuated by the occasional publication of 'decisive' experimental demonstrations supporting one or other of these values. We review the compelling arguments made in support of the Minkowski and Abraham forms and are led to the conclusion that both momenta are correct. We explain why two distinct momenta are needed to describe light in a medium and why each appears as the natural, and experimentally observed, momentum in appropriate situations.
Philosophical Transactions of The Royal Society A Mathematical Physical and Engineering Sciences 03/2010; 368(1914):927-39. · 2.77 Impact Factor
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Stephen M Barnett
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ABSTRACT: The dilemma of identifying the correct form for the momentum of light in a medium has run for a century and has been informed by many distinguished contributions, both theoretical and experimental. We show that both the Abraham and Minkowski forms of the momentum density are correct, with the former being the kinetic momentum and the latter the canonical momentum. This identification allows us to explain why the experiments supporting each of the rival momenta gave the results that they did. The inclusion of dispersion and absorption provides an interesting subtlety, but does not change our conclusion.
Physical Review Letters 02/2010; 104(7):070401. · 7.37 Impact Factor
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ABSTRACT: Using angular-position-orbital-angular-momentum entangled photons, we study angular two-photon interference in a scheme in which entangled photons are made to pass through apertures in the form of double angular slits, and using this scheme, we demonstrate an entangled two-qubit state that is based on the angular-position correlations of entangled photons. The entanglement of the two-qubit state is quantified in terms of concurrence. These results provide an additional means for preparing entangled quantum states for use in quantum information protocols.
Physical Review Letters 01/2010; 104(1):010501. · 7.37 Impact Factor
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ABSTRACT: We investigate the uncertainty associated with a joint quantum measurement of two components of spin of a spin-1/2 particle and quantify this in terms of entropy. We consider two entropic quantities: the joint entropy and the sum of the marginal entropies, and obtain lower bounds for each of these quantities. For the case of joint measurements where we measure each spin observable equally well, these lower bounds are tight. Comment: 13 pages, introduction re-written and extended discussion of results
12/2008;
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ABSTRACT: It is a fundamental consequence of the superposition principle for quantum states that there must exist non-orthogonal states, that is states that, although different, have a non-zero overlap. This finite overlap means that there is no way of determining with certainty in which of two such states a given physical system has been prepared. We review the various strategies that have been devised to discriminate optimally between non-orthogonal states and some of the optical experiments that have been performed to realise these.
11/2008;
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ABSTRACT: We provide a simple proof for the necessity of conditions for discriminating with minimum error between a known set of quantum states. Comment: 4 pages
10/2008;
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ABSTRACT: Different expressions for the linear polarizability of a two-level atom with radiative corrections have been derived recently. We show that an expression said to differ from that obtained by the present authors is in fact consistent with it. The same-sign and opposite-sign prescriptions for linewidths are revisited with respect to the polarizability, the scattering amplitude, and the optical theorem. Both prescriptions represent approximations to more general expressions in the two-level case, and neither is correct for transitions between excited atomic states, as we demonstrate by calculating the linear polarizability of a three-level atom.
Phys. Rev. A. 04/2008; 77(4).
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ABSTRACT: Light emerging from a spiral phase plate with a non-integer phase step has a complicated vortex structure and is unstable on propagation. We generate light carrying fractional orbital angular momentum (OAM) not with a phase step but by a synthesis of Laguerre-Gaussian modes. By limiting the number of different Gouy phases in the superposition we produce a light beam which is well characterised in terms of its propagation. We believe that their structural stability makes these beams ideal for quantum information processes utilising fractional OAM states.
Optics Express 02/2008; 16(2):993-1006. · 3.59 Impact Factor
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ABSTRACT: Quantum correlations do not allow signaling, and any operation which may be performed on one system of an entangled pair cannot be detected by measurement of the other system alone. This no-signaling condition limits allowed operations and, in the context of quantum communication, may be used to put bounds on quantum state discrimination. We find that the natural figure of merit to consider is the confidence in identifying a state, which is optimized by the maximum confidence strategy. We show that this strategy may be derived from the no-signaling condition, and demonstrate the relationship between maximum confidence measurements and entanglement concentration.
Phys. Rev. A. 01/2008; 77(1).
