Showing papers on "Coherent states published in 2007"
TL;DR: In this paper, a spinfoam vertex is introduced to be used in models of 4D quantum gravity based on SU(2) and SO(4) BF theory plus constraints.
Abstract: We introduce a new spinfoam vertex to be used in models of 4d quantum gravity based on SU(2) and SO(4) BF theory plus constraints. It can be seen as the conventional vertex of SU(2) BF theory, the 15j symbol, in a particular basis constructed using SU(2) coherent states. This basis makes the geometric interpretation of the variables transparent: they are the vectors normal to the triangles within each tetrahedron. We study the condition under which these states can be considered semiclassical, and we show that the semiclassical ones dominate the evaluation of quantum correlations. Finally, we describe how the constraints reducing BF to gravity can be directly written in terms of the new variables, and how the semiclassicality of the states might improve understanding the correct way to implement the constraints.
470 citations
Book•
01 Jan 2007
TL;DR: In this article, the authors present a generalization of the Laguerre function to a non-convex version of it, and show that it can be used to derive a deterministic deterministic SI(1,1) operator.
Abstract: PART I - Introduction. 1: Introduction. 1.1 Basic review. 1.2. Motivations and aims. PART II - Method. 2: Theory. 2.1. Introduction. 2.2. Formalism. 3: Lie Algebras SU(2) and SU(1,1). 3.1. Introduction. 3.2. Abstract groups. 3.3. Matrix representation. 3.4. properties of groups SU(2) and SO(3). 3.5. Properties of non-compact groups SO(2,1) and SU(1,1). 3.6. Generators of Lie groups SU(2) and SU(1,1). 3.7. Irreducible representations. 3.8. Irreducible unitary representations. 3.9. Concluding remarks. PART III - Applications in Non-Relativistic Quantum mechanics. 4: Harmonic Oscillator. 4.1. Introduction. 4.2. Exact solutions. 4.3. Ladder operators. 4.4. Bargmann-Segal transformations. 4.5. Single mode realization of dynamic group SU(1,1). 4.6. Matrix elements. 4.7. Coherent states. 4.8. Franck-Condon factors. 4.9. Concluding remarks. 5: Infinitely Deep Square-Well Potential. 5.1. Introduction. 5.2. Ladder operators for infinitely deep square-well potential. 5.3. Realization of dynamic group SU(1,1) and matrix elements. 5.4. Ladder operators for infinitely deep symmetric well potential. 5.5. SUSYQM approach to infinitely deep square-well potential. 5.6. Perelomov coherent states. 5.7. Barut-Girardello coherent states. 5.8. Concluding remarks. 6: Morse Potential. 6.1. Introduction. 6.2. Exact solutions. 6.3. Ladder operators for the Morse potential. 6.4. Realization of dynamic group SU(2). 6.5. Matrix elements. 6.6. Harmonic limit. 6.7. Franck-Condon factors. 6.8. Transition probability. 6.9. Realization of dynamic group SU(1,1). 6.10. Concluding remarks. 7: Poschl-Teller Potential. 7.1. Introduction. 7.2. Exact solutions. 7.3. Ladder operators. 7.4. Realization of dynamic group SU(2). 7.5. Alternative approach to derive ladder operators. 7.6. Harmonic limit. 7.7. Expansions of the coordinate x and momentum p from the SU(2) generators.7.8. Concluding remarks. 8: Pseudoharmonic Oscillator. 8.1. Introduction. 8.2. Exact solutions in one dimension. 8.3. Ladder operators. 8.4. Barut-Girardello coherent states. 8.5. Thermodynamic properties. 8.6. Pseudoharmonic oscillator in arbitrary dimensions. 8.7. Recurrence relations among matrix elements. 8.8. Concluding remarks. 9: Algebraic Approach to an Electron in a Uniform Magnetic Field. 9.1. Introduction. 9.2. Exact solutions. 9.3. Ladder operators. 9.4. Concluding remarks. 10: Ring-Shaped Non-Spherical Oscillator. 10.1. Introduction. 10.2. Exact solutions. 10.3. Ladder operators. 10.4. Realization of dynamic group. 10.5. Concluding remarks. 11: Generalized Laguerre Functions. 11.1. Introduction. 11.2. generalized Laguerre functions. 11.3. Ladder operators and realization of dynamic group SU(1,1). 11.4. Concluding remarks. 12: New Non-Central Ring-Shaped Potential. 12.1. Introduction. 12.2. Bound states. 12.3. Ladder operators. 12.4. Mean values. 12.5. Continuum states. 12.6. Concluding remarks. 13: Poschl-Teller Like Potential. 13.1. Introduction. 13.2. Exact solutions. 13.3. Ladder operators. 13.4. Realization of dynamic group and matrix elements. 13.5. Infinitely square-well and harmonic limits. 13.6. Concluding remarks. 14: Position-Dependent Mass Schrodinger Equation for a Singular Oscillator. 14.1. Introduction. 14.2. Position-dependent effective mass Schrodinger equation for harmonic oscillator. 14.3. Singular oscillator with a position-dependent effective mass. 14.4. Complete solutions. 14.5. Another position-dependent effective mass. 14.6. Concluding remarks. PART IV - Applications in Relativistic Quantum Mechanics. 15: SUSYQM and SKWB Approach to the Dirac Equation with a Coulomb Potential in 2+1 Dimensions. 15.1. Introduction. 15.2. Dirac equation in 2+1 dimensions. 15.3. Exact solutions. 15.4. SUSYQM
386 citations
TL;DR: The observation of spontaneous build-up of in-phase and antiphase ‘superfluid’ states in a solid-state system; an array of exciton–polariton condensates connected by weak periodic potential barriers within a semiconductor microcavity.
Abstract: A microcavity structure to which a periodic potential is applied has been designed, which effectively creates an array of weakly-coupled condensates. This allows the observation of fundamental dynamic behaviour, namely the build-up of certain superfluid-like states, which has been predicted for arrays of atomic Bose–Einstein condensates, but not yet observed. The effect of quantum statistics in quantum gases and liquids results in observable collective properties among many-particle systems. One prime example is Bose–Einstein condensation, whose onset in a quantum liquid leads to phenomena such as superfluidity and superconductivity. A Bose–Einstein condensate is generally defined as a macroscopic occupation of a single-particle quantum state, a phenomenon technically referred to as off-diagonal long-range order due to non-vanishing off-diagonal components of the single-particle density matrix1,2,3. The wavefunction of the condensate is an order parameter whose phase is essential in characterizing the coherence and superfluid phenomena4,5,6,7,8,9,10,11. The long-range spatial coherence leads to the existence of phase-locked multiple condensates in an array of superfluid helium12, superconducting Josephson junctions13,14,15 or atomic Bose–Einstein condensates15,16,17,18. Under certain circumstances, a quantum phase difference of π is predicted to develop among weakly coupled Josephson junctions19. Such a meta-stable π-state was discovered in a weak link of superfluid 3He, which is characterized by a ‘p-wave’ order parameter20. The possible existence of such a π-state in weakly coupled atomic Bose–Einstein condensates has also been proposed21, but remains undiscovered. Here we report the observation of spontaneous build-up of in-phase (‘zero-state’) and antiphase (‘π-state’) ‘superfluid’ states in a solid-state system; an array of exciton–polariton condensates connected by weak periodic potential barriers within a semiconductor microcavity. These in-phase and antiphase states reflect the band structure of the one-dimensional polariton array and the dynamic characteristics of metastable exciton–polariton condensates.
361 citations
TL;DR: This experiment demonstrates the reversible mapping of a coherent state of light with a mean photon number approximately equal to 1.1 to and from the hyperfine states of an atom trapped within the mode of a high-finesse optical cavity.
Abstract: We demonstrate the reversible mapping of a coherent state of light with a mean photon number (-)n approximately equal to 1.1 to and from the hyperfine states of an atom trapped within the mode of a high-finesse optical cavity. The coherence of the basic processes is verified by mapping the atomic state back onto a field state in a way that depends on the phase of the original coherent state. Our experiment represents an important step toward the realization of cavity QED-based quantum networks, wherein coherent transfer of quantum states enables the distribution of quantum information across the network.
262 citations
TL;DR: Nonclassicality of the generated states clearly shows up as its negative region around the origin of the phase-space distributions, i.e., the Wigner functions, which is largest ever observed without any correction for experimental imperfections.
Abstract: We present generation of photon-subtracted squeezed states at 860 nm, from nearly pure, continuous-wave squeezed vacua generated with a periodically-poled KTiOPO4 crystal as a nonlinear medium of a subthreshold optical parametric oscillator. We observe various kinds of photon-subtracted squeezed states, including non-Gaussian states similar to the single-photon state and superposition states of coherent states, simply by changing the pump power. Nonclassicality of the generated states clearly shows up as its negative region around the origin of the phase-space distributions, i.e., the Wigner functions. We obtain the value, -0.083 at the origin of the Wigner function, which is largest ever observed without any correction for experimental imperfections.
230 citations
TL;DR: A review of theoretical and experimental aspects of multiphoton quantum optics can be found in this paper, where the authors concentrate their attention on parametric processes in nonlinear media, with special emphasis on the engineering of nonclassical states of photons and atoms.
Abstract: We present a review of theoretical and experimental aspects of multiphoton quantum optics. Multiphoton processes occur and are important for many aspects of matter-radiation interactions that include the efficient ionization of atoms and molecules, and, more generally, atomic transition mechanisms; system-environment couplings and dissipative quantum dynamics; laser physics, optical parametric processes, and interferometry. A single review cannot account for all aspects of such an enormously vast subject. Here we choose to concentrate our attention on parametric processes in nonlinear media, with special emphasis on the engineering of nonclassical states of photons and atoms. We present a detailed analysis of the methods and techniques for the production of genuinely quantum multiphoton processes in nonlinear media, and the corresponding models of multiphoton effective interactions. We review existing proposals for the classification, engineering, and manipulation of nonclassical states, including Fock states, macroscopic superposition states, and multiphoton generalized coherent states. We introduce and discuss the structure of canonical multiphoton quantum optics and the associated one- and two-mode canonical multiphoton squeezed states. This framework provides a consistent multiphoton generalization of two-photon quantum optics and a consistent Hamiltonian description of multiphoton processes associated to higher-order nonlinearities. Finally, we discuss very recent advances that by combining linear and nonlinear optical devices allow to realize multiphoton entangled states of the electromnagnetic field, that are relevant for applications to efficient quantum computation, quantum teleportation, and related problems in quantum communication and information.
200 citations
TL;DR: A "counterintuitive" regime is found in which the evolution of the condensate when the splitting is sufficiently slow is not to the fragmented ground state, but to a low-lying excited state which is a coherent state.
Abstract: An essentially exact approach to compute the wave function in the time-dependent many-boson Schrodinger equation is derived and employed to study accurately the process of splitting a trapped condensate. As the trap transforms from a single to double well the ground state changes from a coherent to a fragmented state. We follow the role played by many-body excited states during the splitting process. Among others, a "counterintuitive" regime is found in which the evolution of the condensate when the splitting is sufficiently slow is not to the fragmented ground state, but to a low-lying excited state which is a coherent state. Experimental implications are discussed.
193 citations
Book•
09 Apr 2007
TL;DR: In this article, the authors present an analysis of the effect of interference on the phase-space distribution of a laser field with respect to a single photon detector and a single phase.
Abstract: 1 The Quantum Theory of Optical Coherence. 1.1 Introduction. 1.2 Elements of Field Theory. 1.3 Field Correlations. 1.4 Coherence. 1.5 Coherence and Polarization. 2 Optical Coherence and Photon Statistics. 2.1 Introduction. 2.1.1 Classical Theory. 2.2 Interference Experiments. 2.3 Introduction of Quantum Theory. 2.4 The One-Atom Photon Detector. 2.5 The n-Atom Photon Detector. 2.6 Properties of the Correlation Functions. 2.6.1 Space and Time Dependence of the Correlation Functions. 2.7 Diffraction and Interference. 2.7.1 Some General Remarks on Interference. 2.7.2 First-Order Coherence. 2.7.3 Fringe Contrast and Factorization. 2.8 Interpretation of Intensity Interferometer Experiments. 2.8.1 Higher Order Coherence and Photon Coincidences. 2.8.2 Further Discussion of Higher Order Coherence. 2.8.3 Treatment of Arbitrary Polarizations. 2.9 Coherent and Incoherent States of the Radiation Field. 2.9.1 Introduction. 2.9.2 Field-Theoretical Background. 2.9.3 Coherent States of a Single Mode. 2.9.4 Expansion of Arbitrary States in Terms of Coherent States. 2.9.5 Expansion of Operators in Terms of Coherent State Vectors. 2.9.6 General Properties of the Density Operator. 2.9.7 The P Representation of the Density Operator. 2.9.8 The Gaussian Density Operator. 2.9.9 Density Operators for the Field. 2.9.10 Correlation and Coherence Properties of the Field. 2.10 Radiation by a Predetermined Charge-Current Distribution. 2.11 Phase-Space Distributions for the Field. 2.11.1 The P Representation and the Moment Problem. 2.11.2 A Positive-Definite "Phase Space Density". 2.11.3 Wigner's "Phase Space Density". 2.12 Correlation Functions and Quasiprobability Distributions. 2.12.1 First Order Correlation Functions for Stationary Fields. 2.12.2 Correlation Functions for Chaotic Fields. 2.12.3 Quasiprobability Distribution for the Field Amplitude. 2.12.4 Quasiprobability Distribution for the Field Amplitudes at Two Space-Time Points. 2.13 Elementary Models of Light Beams. 2.13.1 Model for Ideal Laser Fields. 2.13.2 Model of a Laser Field With Finite Bandwidth. 2.14 Interference of Independent Light Beams. 2.15 Photon Counting Experiments. References. 3 Correlation Functions for Coherent Fields. 3.1 Introduction. 3.2 Correlation Functions and Coherence Conditions. 3.3 Correlation Functions as Scalar Products. 3.4 Application to Higher Order Correlation Functions. 3.5 Fields With Positive-Definite P Functions. References. 4 Density Operators for Coherent Fields. 4.1 Introduction. 4.2 Evaluation of the Density Operator. 4.3 Fully Coherent Fields. 4.4 Unique Properties of the Annihilation Operator Eigenstates. 5 Classical Behavior of Systems of Quantum Oscillators. 6 Quantum Theory of Parametric Amplification I. 6.1 Introduction. 6.2 The Coherent States and the P Representation. 6.3 Model of the Parametric Amplifier. 6.4 Reduced Density Operator for the A Mode. 6.5 Initially Coherent State: P Representation for the A Mode. 6.6 Initially Coherent State Moments, Matrix Elements, and Explicit Representation for pA(t). 6.7 Solutions for an Initially Chaotic B Mode. 6.8 Solution for Initial n-Quantum State of A Mode B Mode Chaotic. 6.9 General Discussion of Amplification With B Mode Initially Chaotic. 6.10 Discussion of P Representation: Characteristic Functions Initially Gaussian. 6.11 Some General Properties of P(alpha, t). 7 Quantum Theory of Parametric Amplification II. 7.1 Introduction. 7.2 The Two-Mode Characteristic Function. 7.3 The Wigner Function. 7.4 Decoupled Equations of Motion. 7.5 Characteristic Functions Expressed in Terms of Decoupled Variables. 7.6 W and P Expressed in Terms of Decoupled Variables. 7.7 Results for Chaotic Initial States. 7.8 Correlations of the Mode Amplitudes. References. 8 Photon Statistics. 8.1 Introduction. 8.2 Classical Theory. 8.3 Quantum Theory: Introduction. 8.4 Intensity and Coincidence Measurements. 8.5 First and Higher Order Coherence. 8.6 The Coherent States. 8.7 Expansions in Terms of the Coherent States. 8.8 Characteristic Functions and Quasiprobability Densities. 8.9 Some Examples. 8.10 Photon Counting Distributions. 9 Ordered Expansions in Boson Amplitude Operators. 9.1 Introduction. 9.2 Coherent States and Displacement Operators. 9.3 Completeness of Displacement Operators. 9.4 Ordered Power-Series Expansions. 9.5 s-Ordered Power-Series Expansions. 9.6 Integral Expansions for Operators. 9.7 Correspondences Between Operators and Functions . 9.8 Illustration of Operator-Function Correspondences. 10 Density Operators and Quasiprobability Distributions. 10.1 Introduction. 10.2 Ordered Operator Expansions. 10.3 The P Representation. 10.4 Wigner Distribution. 10.5 The Function (&alpha , p, &alpha ) . 10.6 Ensemble Averages and s Ordering. 10.7 Examples of the General Quasiprobability Function W (&alpha , s). 10.8 Analogy with Heat Diffusion. 10.9 Time-Reversed Heat Diffusion and W (&alpha , s). 10.10 Properties Common to all Quasiprobability Distributions. 11 Coherence and Quantum Detection. 11.1 Introduction. 11.2 The Statistical Properties of the Electromagnetic Field. 11.3 The Ideal Photon Detector. 11.4 Correlation Functions and Coherence. 11.5 Other Correlation Functions. 11.6 The Coherent States. 11.7 Expansions in Terms of Coherent States. 11.8 A Few General Observations. 11.9 The Damped Harmonic Oscillator. 11.10 The Density Operator for the Damped Oscillator. 11.11 Irreversibility and Damping. 11.12 The Fokker-Planck and Bloch Equations. 11.13 Theory of Photodetection. The Photon Counter Viewed as a Harmonic Oscillator. 11.14 The Density Operator for the Photon Counter. 12 Quantum Theory of Coherence. 12.1 Introduction. 12.2 Classical Theory. 12.3 Quantum Theory. 12.4 Intensity and Coincidence Measurements. 12.5 Coherence. 12.6 Coherent States. 12.7 The P Representation. 12.8 Chaotic States. 12.9 Wavepacket Structure of Chaotic Field. 13 The Initiation of Superfluorescence. 13.1 Introduction. 13.2 Basic Equations for a Simple Model. 13.3 Onset of Superfluorescence. 14 Amplifiers, Attenuators and Schr .. odingers Cat. 14.1 Introduction: Two Paradoxes. 14.2 A Quantum-Mechanical Attenuator: The Damped Oscillator. 14.3 A Quantum Mechanical Amplifier. 14.4 Specification of Photon Polarization States. 14.5 Measuring Photon Polarizations. 14.6 Use of the Compound Amplifier. 14.7 Superluminal Communication? 14.8 Interference Experiments and Schr..odinger's Cat. 15 The Quantum Mechanics of Trapped Wavepackets. 15.1 Introduction. 15.2 Equations of Motion and Their Solutions. 15.3 The Wave Functions. 15.4 Periodic Fields and Trapping. 15.5 Interaction With the Radiation Field. 15.6 Sum Rules. 15.7 Radiative Equilibrium and Instability. 16 Density Operators for Fermions. 16.1 Introduction. 16.2 Notation. 16.3 Coherent States for Fermions. 16.3.1 Displacement Operators. 16.3.2 Coherent States. 16.3.3 Intrinsic Descriptions of Fermionic States. 16.4 Grassmann Calculus. 16.4.1 Differentiation. 16.4.2 Even and Odd Functions. 16.4.3 Product Rule. 16.4.4 Integration. 16.4.5 Integration by Parts. 16.4.6 Completeness of the Coherent States. 16.4.7 Completeness of the Displacement Operators. 16.5 Operators. 16.5.1 The Identity Operator. 16.5.2 The Trace. 16.5.3 Physical States and Operators. 16.5.4 Physical Density Operators. 16.6 Functions and Fourier Transforms. 16.7 Operator Expansions. 16.8 Characteristic Functions. 16.8.1 The s-Ordered Characteristic Function. 16.9 s-Ordered Expansions for Operators. 16.10 Quasiprobability Distributions. 16.11 Mean Values of Operators. 16.12 P Representation. 16.13 Correlation Functions for Fermions. 16.14 Chaotic States of the Fermion Field. 16.15 Correlation Functions for Chaotic Field Excitations. 16.16 Fermion-Counting Experiments. 16.17 Some Elementary Examples. 16.17.1 The Vacuum State. 16.17.2 A Physical Two-Mode Density Operator. Index.
148 citations
TL;DR: In this paper, the effects of a nearly uniform Bose-Einstein condensate (BEC) on the properties of trapped impurity atoms were investigated, and it was shown that the transport properties of the impurities change from coherent to diffusive.
Abstract: We investigate the effects of a nearly uniform Bose-Einstein condensate (BEC) on the properties of immersed trapped impurity atoms. Using a weak-coupling expansion in the BEC-impurity interaction strength, we derive a model describing polarons, i.e., impurities dressed by a coherent state of Bogoliubov phonons, and apply it to ultracold bosonic atoms in an optical lattice. We show that, with increasing BEC temperature, the transport properties of the impurities change from coherent to diffusive. Furthermore, stable polaron clusters are formed via a phonon-mediated off-site attraction.
143 citations
Book•
01 Jan 2007
TL;DR: Two-photon interference in parametric down-conversion has been studied in this paper, where the phase independent interference between a two-phase state and a coherent state has been investigated.
Abstract: Two-Photon Interference.- Historical Background and General Remarks.- Quantum State from Parametric Down-Conversion.- Hong-Ou-Mandel Interferometer.- Phase-Independent Two-Photon Interference.- Phase-Dependent Two-Photon Interference: Two-Photon Interferometry.- Interference between a Two-Photon State and~a Coherent State.- Quantum Interference of More Than Two Photons.- Coherence and Multiple Pair Production in~Parametric Down-Conversion.- Quantum Interference with Two Pairs of~Down-Converted Photons.- Temporal Distinguishability of a Multi-Photon State.- Homodyne of a Single-Photon State: A Special Multi-Photon Interference.
127 citations
TL;DR: In this article, the position-dependent mass oscillator is studied from both, classical and quantum mechanical points of view, in order to discuss the ambiguity on the operator ordering of the kinetic term in the quantum framework.
TL;DR: A Bayesian phase estimation strategy is explored to demonstrate that it is possible to achieve the standard quantum limit independently from the true value of the phase shift and specific assumptions on the noise of the interferometer.
Abstract: We study a Mach-Zehnder interferometer fed by a coherent state in one input port and vacuum in the other. We explore a Bayesian phase estimation strategy to demonstrate that it is possible to achieve the standard quantum limit independently from the true value of the phase shift and specific assumptions on the noise of the interferometer. We have been able to implement the protocol by using parallel operation of two photon-number-resolving detectors and multiphoton coincidence logic electronics at the output ports of a weakly illuminated Mach-Zehnder interferometer. This protocol is unbiased, saturates the Cramer-Rao phase uncertainty bound, and, therefore, is an optimal phase estimation strategy.
TL;DR: It is shown that thermal wave relaxation to equilibrium may be characterized by the existence of a genuine condensation process, whose thermodynamic properties are analogous to those of Bose-Einstein condensation, despite the fact that the considered optical wave is completely classical.
Abstract: This concise review is aimed at providing an introduction to the kinetic theory of partially coherent optical waves propagating in nonlinear media. The subject of incoherent nonlinear optics received a renewed interest since the first experimental demonstration of incoherent solitons in slowly responding photorefractive crystals. Several theories have been successfully developed to provide a detailed description of the novel dynamical features inherent to partially coherent nonlinear optical waves. However, such theories leave unanswered the following important question: Which is the long term (spatiotemporal) evolution of a partially incoherent optical field propagating in a nonlinear medium? In complete analogy with kinetic gas theory, one may expect that the incoherent field may evolve, owing to nonlinearity, towards a thermodynamic equilibrium state. Weak-turbulence theory is shown to describe the essential properties of this irreversible process of thermal wave relaxation to equilibrium. Precisely, the theory describes an irreversible evolution of the spectrum of the field towards a thermodynamic equilibrium state. The irreversible behavior is expressed through the H-theorem of entropy growth, whose origin is analogous to the celebrated Boltzmann’s H-theorem of kinetic gas theory. It is shown that thermal wave relaxation to equilibrium may be characterized by the existence of a genuine condensation process, whose thermodynamic properties are analogous to those of Bose-Einstein condensation, despite the fact that the considered optical wave is completely classical. In spite of the formal reversibility of optical wave propagation, the condensation process occurs by means of an irreversible evolution of the field towards a homogeneous plane-wave (condensate) with small-scale fluctuations superimposed (uncondensed particles), which store the information necessary for the reversible propagation. As a remarkable result, an increase of entropy (“disorder”) in the optical field requires the generation of a coherent structure (plane-wave). We show that, beyond the standard thermodynamic limit, wave condensation also occurs in two spatial dimensions. The numerical simulations are in quantitative agreement with the kinetic wave theory, without any adjustable parameter.
TL;DR: In this paper, a new model is studied which describes the quantum behavior of transitions through an isotropic quantum cosmological bounce in loop quantum cosmology sourced by a free and massless scalar field.
Abstract: A new model is studied which describes the quantum behavior of transitions through an isotropic quantum cosmological bounce in loop quantum cosmology sourced by a free and massless scalar field. As an exactly solvable model even at the quantum level, it illustrates properties of dynamical coherent states and provides the basis for a systematic perturbation theory of loop quantum gravity. The detailed analysis is remarkably different from what is known for harmonic oscillator coherent states. Results are evaluated with regard to their implications in cosmology, including a demonstration that in general quantum fluctuations before and after the bounce are unrelated. Thus, even within this solvable model the condition of classicality at late times does not imply classicality at early times before the bounce without further assumptions. Nevertheless, the quantum state does evolve deterministically through the bounce.
TL;DR: In this article, the authors derived coherent states for one-dimensional systems generated by supersymmetry from an initial Hamiltonian with a purely discrete spectrum for which the levels depend analytically on their subindex.
Abstract: Coherent states are derived for one-dimensional systems generated by supersymmetry from an initial Hamiltonian with a purely discrete spectrum for which the levels depend analytically on their subindex. It is shown that the algebra of the initial system is inherited by its SUSY partners in the subspace associated to the isospectral part or the spectrum. The technique is applied to the harmonic oscillator, infinite well and trigonometric Poeschl-Teller potentials.
TL;DR: In this article, the authors derived coherent states for one-dimensional systems generated by supersymmetry from an initial Hamiltonian with a purely discrete spectrum for which the levels depend analytically on their subindex.
Abstract: Coherent states are derived for one-dimensional systems generated by supersymmetry from an initial Hamiltonian with a purely discrete spectrum for which the levels depend analytically on their subindex. It is shown that the algebra of the initial system is inherited by its SUSY partners in the subspace associated with the isospectral part or the spectrum. The technique is applied to the harmonic oscillator, infinite well and trigonometric Poschl–Teller potentials.
TL;DR: It is shown that a linear superposition of mesoscopic states in relativistic Landau levels can be built when an external magnetic field couples to a relativist spin 1/2 charged particle.
Abstract: We show that a linear superposition of mesoscopic states in relativistic Landau levels can be built when an external magnetic field couples to a relativistic spin 1/2 charged particle. Under suitable initial conditions, the associated Dirac equation produces unitarily superpositions of coherent states involving the particle orbital quanta in a well-defined mesoscopic regime. We demonstrate that these mesoscopic superpositions have a purely relativistic origin and disappear in the nonrelativistic limit.
TL;DR: This work proves the security of the Bennett-Brassard (BB84) quantum key distribution protocol in the case where the key information is encoded in the relative phase of a coherent- state reference pulse and a weak coherent-state signal pulse, as in some practical implementations of the protocol.
Abstract: We prove the security of the Bennett-Brassard (BB84) quantum key distribution protocol in the case where the key information is encoded in the relative phase of a coherent-state reference pulse and a weak coherent-state signal pulse, as in some practical implementations of the protocol. In contrast to previous work, our proof applies even if the eavesdropper knows the phase of the reference pulse, provided that this phase is not modulated by the source, and even if the reference pulse is bright. The proof also applies to the case where the key is encoded in the photon polarization of a weak coherent-state pulse with a known phase, but only if the phases of the four BB84 signal states are judiciously chosen. The achievable key generation rate scales quadratically with the transmission in the channel, just as for BB84 with phase-randomized weak coherent-state signals (when decoy states are not used). For the case where the phase of the reference pulse is strongly modulated by the source, we exhibit an explicit attack that allows the eavesdropper to learn every key bit in a parameter regime where a protocol using phase-randomized signals is provably secure.
TL;DR: In this article, a decoy-state method with a heralded single-photon source for QKD was proposed and the final key rate over transmission distance was simulated under various parameter sets.
Abstract: We propose a practical decoy-state method with heralded single-photon source for quantum key distribution (QKD). In the protocol, three intensities are used and one can estimate the fraction of single-photon counts. The final key rate over transmission distance is simulated under various parameter sets. Due to the lower dark count than that of a coherent state, it is shown that a three-intensity decoy-state QKD with a heralded source can work for a longer distance than that of a coherent state.
TL;DR: A similarity transformation between the XY Hamiltonian and the double-quantum Hamiltonian is presented, an interaction which is achievable with the collective control provided by radio-frequency pulses and makes it possible to study experimentally the transport of polarization beyond exactly solvable models and explore the appearance of quantum coherence and interference effects.
Abstract: Transport of quantum information in linear spin chains has been the subject of much theoretical work. Experimental studies by NMR in solid state spin systems (a natural implementation of such models) is complicated since the dipolar Hamiltonian is not solely comprised of nearest-neighbor $XY$-Heisenberg couplings. We present here a similarity transformation between the $XY$ Hamiltonian and the double-quantum Hamiltonian, an interaction which is achievable with the collective control provided by radio-frequency pulses. Not only can this second Hamiltonian simulate the information transport in a spin chain, but it also creates coherent states, whose intensities give an experimental signature of the transport. This scheme makes it possible to study experimentally the transport of polarization beyond exactly solvable models and explore the appearance of quantum coherence and interference effects.
TL;DR: In this article, it was shown that two-mode entangled coherent states with coherent amplitudes as small as 0.842 are sufficient to produce Bell inequality violations up to Tsirelson's bound.
Abstract: We find that Bell's inequality can be significantly violated (up to Tsirelson's bound) with two-mode entangled coherent states using only homodyne measurements. This requires Kerr nonlinear interactions for local operations on the entangled coherent states. Our example is a demonstration of Bell-inequality violations using classical measurements. We conclude that entangled coherent states with coherent amplitudes as small as 0.842 are sufficient to produce such violations.
TL;DR: In this article, Filip et al. demonstrate a universal, deterministic, and high-fidelity squeezing transformation of an optical field, which relies only on linear optics, homodyne detection, feedforward, and an ancillary squeezed vacuum state.
Abstract: By employing a recent proposal [R. Filip, P. Marek, and U.L. Andersen, Phys. Rev. A 71, 042308 (2005)] we experimentally demonstrate a universal, deterministic, and high-fidelity squeezing transformation of an optical field. It relies only on linear optics, homodyne detection, feedforward, and an ancillary squeezed vacuum state, thus direct interaction between a strong pump and the quantum state is circumvented. We demonstrate three different squeezing levels for a coherent state input. This scheme is highly suitable for the fault-tolerant squeezing transformation in a continuous variable quantum computer.
TL;DR: In this paper, a model of charge transport in organic molecular semiconductors based on the effects of lattice fluctuations on the quantum coherence of the electronic state of the charge carrier is presented.
Abstract: We present a model of charge transport in organic molecular semiconductors based on the effects of lattice fluctuations on the quantum coherence of the electronic state of the charge carrier. Thermal intermolecular phonons and librations tend to localize pure coherent states and to assist the motion of less coherent ones. Decoherence is thus the primary mechanism by which conduction occurs. It is driven by the coupling of the carrier to the molecular lattice through polarization and transfer integral fluctuations as described by the hamiltonian of Gosar and Choi. Localization effects in the quantum coherent regime are modeled via the Anderson hamiltonian with correlated diagonal and non-diagonal disorder leading to the determination of the carrier localization length. This length defines the coherent extension of the ground state and determines, in turn, the diffusion range in the incoherent regime and thus the mobility. The transfer integral disorder of Troisi and Orlandi can also be incorporated. This model, based on the idea of decoherence, allowed us to predict the value and temperature dependence of the carrier mobility in prototypical organic semiconductors that are in qualitative accord with experiments.
TL;DR: In this paper, a quantum mechanical gyroscope is used as a reference against which to measure the angular momenta of spin-1/2 particles, and the reference thermalizes with the measured particles and finds that the thermal state is reached in a time which scales linearly with the size of the reference.
Abstract: We analyse a quantum mechanical gyroscope which is modelled as a large spin and used as a reference against which to measure the angular momenta of spin-1/2 particles. These measurements induce a back-action on the reference which is the central focus of our study. We begin by deriving explicit expressions for the quantum channel representing the back-action. Then, we analyse the dynamics incurred by the reference when it is used to sequentially measure particles drawn from a fixed ensemble. We prove that the reference thermalizes with the measured particles and find that generically, the thermal state is reached in a time which scales linearly with the size of the reference. This contrasts with a recent conclusion of Bartlett et al that this takes a quadratic amount of time when the particles are completely unpolarized. We now understand their result in terms of a simple physical principle based on symmetries and conservation laws. Finally, we initiate the study of the non-equilibrium dynamics of the reference. Here we find that a reference in a coherent state will essentially remain in one when measuring polarized particles, while rotating itself to ultimately align with the polarization of the particles.
TL;DR: In this paper, the creation and annihilation operators of pseudo-hermitian fermions for two-level systems described by a pseudo-Hermitian Hamiltonian with real eigenvalues are introduced.
Abstract: We introduce creation and annihilation operators of pseudo-Hermitian fermions for two-level systems described by a pseudo-Hermitian Hamiltonian with real eigenvalues. This allows the generalization of the fermionic coherent states approach to such systems. Pseudo-fermionic coherent states are constructed as eigenstates of two pseudo-fermion annihilation operators. These coherent states form a bi-normal and bi-overcomplete system, and their evolution governed by the pseudo-Hermitian Hamiltonian is temporally stable. In terms of the introduced pseudo-fermion operators, the two-level system Hamiltonian takes a factorized form similar to that of a harmonic oscillator.
TL;DR: In this paper, the authors proposed a method to generate entangled coherent states between two spatially separated atomic Bose-Einstein condensates via the technique of electromagnetically induced transparency (EIT).
Abstract: We propose a method to generate entangled coherent states between two spatially separated atomic Bose-Einstein condensates (BECs) via the technique of electromagnetically induced transparency (EIT). Two strong coupling laser beams and two entangled probe laser beams are used to cause two distant BECs to be in EIT states and to generate an atom-photon entangled state between probe lasers and distant BECs. The two BECs are initially in unentangled product coherent states while the probe lasers are initially in an entangled state. Entangled states of two distant BECs can be created through the performance of projective measurements upon the two outgoing probe lasers under certain conditions. Concretely, we propose two protocols to show how to generate entangled coherent states of the two distant BECs. One is a single-photon scheme in which an entangled single-photon state is used as the quantum channel to generate entangled distant BECs. The other is a multiphoton scheme where an entangled coherent state of the probe lasers is used as the quantum channel. Additionally, we also obtain some atom-photon entangled states of particular interest such as entangled states between a pair of optical Bell states (or quasi-Bell-states) and a pair of atomic entangled coherent states (or quasi-Bell-states).
TL;DR: Theory and experimentally observe the behavior outside the Lamb-Dicke regime, where the trajectory in phase space is modified and the motional coherent states become squeezed, and directly observe the modification of the return time of the trajectory and infer the squeezing.
Abstract: We create entangled states of the spin and motion of a single 40Ca+ ion in a linear ion trap. We theoretically study and experimentally observe the behavior outside the Lamb-Dicke regime, where the trajectory in phase space is modified and the motional coherent states become squeezed. We directly observe the modification of the return time of the trajectory, and infer the squeezing. The mesoscopic entanglement is observed up to Deltaalpha=5.1 with coherence time 170 micros and mean phonon excitation n = 16.
TL;DR: This work analyzes two sequential attacks based on unambiguous state discrimination and minimum error discrimination of the signal states emitted by the source of pulsed coherent light to determine the ultimate upper bounds on the maximal distance achievable by quantum key distribution schemes.
Abstract: We investigate limitations imposed by sequential attacks on the performance of differential-phase-shift quantum key distribution protocols that use pulsed coherent light. In particular, we analyze two sequential attacks based on unambiguous state discrimination and minimum error discrimination, respectively, of the signal states emitted by the source. Sequential attacks represent a special type of intercept-resend attacks and, therefore, they provide ultimate upper bounds on the maximal distance achievable by quantum key distribution schemes.
TL;DR: In this article, an exact algebraic solution of a single graphene plane in transverse electric and perpendicular magnetic fields is presented, which gives both the eigenvalues and the Eigenfunctions of the graphene plane.
Abstract: We present an exact algebraic solution of a single graphene plane in transverse electric and perpendicular magnetic fields. The method presented gives both the eigen-values and the eigen-functions of the graphene plane. It is shown that the eigen-states of the problem can be casted in terms of coherent states, which appears in a natural way from the formalism.
TL;DR: A method for a weak continuous measurement of the energy eigenstates of a fast quantum system by means of a slow detector that is sensitive only to slowly changing variables and can be limited solely to decoherence of the eigenstate superpositions is proposed.
Abstract: We propose a method for a weak continuous measurement of the energy eigenstates of a fast quantum system by means of a slow detector. Such a detector is sensitive only to slowly changing variables, e.g., energy, while its backaction can be limited solely to decoherence of the eigenstate superpositions. We apply this scheme to the problem of detection of quantum jumps between energy eigenstates in a harmonic oscillator.