Showing papers on "Coherent states published in 2009"
Book•
26 Oct 2009
TL;DR: In this article, the basic formalism of Probability theory has been used for the quantization of spin-coherent states in the context of quantum information and quantum physics.
Abstract: Part I: Coherent States 1. Introduction 2. The Standard Coherent States: The Basics 3. The Standard Coherent States: The (Elementary) Mathematics 4. Coherent States in Quantum Information: An Example of Experimental Manipulation 5. Coherent States: A General Construction 6. The Spin Coherent States 7. Selected Pieces of Applications of Standard and Spin Coherent States 8. SU(1,1) or SL(2,R)Coherent States 9. Another Family of SU(1,1) Coherent States for Quantum Systems 10. Squeezed States and their SU(1,1) Content 11. Fermionic Coherent States Part II: Coherent State Quantization 12. Standard Coherent Quantization: The Klauder-Berezin Approach 13. Coherent State or Frame Quantization 14. CS Quantization of Finite Set, Unit Interval, and Circle 15. CS Quantization of Motions on Circle, Interval, and Others 16. Quantization of the Motion on the Torus 17. Fuzzy Geometries: Sphere and Hyperboloid 18. Conclusion and Outlook Appendices A. The Basic Formalism of Probability Theory B. The Basics of Lie Algebra, Lie Groups, and their Representation C. SU(2)-Material D. Wigner-Eckart Theorem for CS quantized Spin Harmonics E. Symmetrization of the Commutator Bibliography
448 citations
361 citations
TL;DR: In this article, a phase space representation of quantum dynamics of systems with many degrees of freedom is discussed, based on a perturbative expansion in quantum fluctuations around one of the classical limits.
Abstract: We discuss a phase space representation of quantum dynamics of systems with many degrees of freedom. This representation is based on a perturbative expansion in quantum fluctuations around one of the classical limits. We explicitly analyze expansions around three such limits: (i) corpuscular or Newtonian limit in the coordinate-momentum representation, (ii) wave or Gross-Pitaevskii limit for interacting bosons in the coherent state representation, and (iii) Bloch limit for the spin systems. We discuss both the semiclassical (truncated Wigner) approximation and further quantum corrections appearing in the form of either stochastic quantum jumps along the classical trajectories or the nonlinear response to such jumps. We also discuss how quantum jumps naturally emerge in the analysis of non-equal time correlation functions. This representation of quantum dynamics is closely related to the phase space methods based on the Wigner-Weyl quantization and to the Keldysh technique. We show how such concepts as the Wigner function, Weyl symbol, Moyal product, Bopp operators, and others automatically emerge from the Feynmann's path integral representation of the evolution in the Heisenberg representation. We illustrate the applicability of this expansion with various examples mostly in the context of cold atom systems including sine-Gordon model, one- and two-dimensional Bose Hubbard model, Dicke model and others.
349 citations
TL;DR: In this paper, the convergence of the quantum Bose gas dynamics to the Hartree equation was shown for a class of singular interaction potentials including the Coulomb potential, and it was shown that the mean-field limit is a "semi-classical" limit.
Abstract: In the mean-field limit the dynamics of a quantum Bose gas is described by a Hartree equation. We present a simple method for proving the convergence of the microscopic quantum dynamics to the Hartree dynamics when the number of particles becomes large and the strength of the two-body potential tends to 0 like the inverse of the particle number. Our method is applicable for a class of singular interaction potentials including the Coulomb potential. We prove and state our main result for the Heisenberg- picture dynamics of “observables”, thus avoiding the use of coherent states. Our formulation shows that the mean-field limit is a “semi-classical” limit.
199 citations
25 Jun 2009
TL;DR: The suppression of nuclear field fluctuations in a singly charged quantum dot to well below the thermal value is reported, as shown by an enhancement of the single electron spin dephasing time T2*, which is measured using coherent dark-state spectroscopy.
Abstract: We report the suppression of nuclear spin fluctuations in a self assembled quantum dot via coherent dark state spectroscopy, resulting in a factor of 40 enhancement of the coherence time of a single electron spin.
194 citations
TL;DR: This model captures the essential characteristics of a class of co-evolving and adaptive networks and exhibits three kinds of asymptotic behavior: a two-cluster state, a coherent state with a fixed phase relation, and a chaotic state with frustration.
Abstract: We investigate co-evolving dynamics in a weighted network of phase oscillators in which the phases of the oscillators at the nodes and the weights of the links interact with each other. We find that depending on the type of the dynamics of the weights, the system exhibits three kinds of asymptotic behavior: a two-cluster state, a coherent state with a fixed phase relation, and a chaotic state with frustration. Because of its structural stability, it is believed that our model captures the essential characteristics of a class of co-evolving and adaptive networks.
143 citations
TL;DR: In this article, a modification of the Kuramoto model incorporating a distribution of interaction delays is proposed to discover generic effects of heterogeneous communication delays on the dynamics of large systems of coupled oscillators.
Abstract: In order to discover generic effects of heterogeneous communication delays on the dynamics of large systems of coupled oscillators, this Letter studies a modification of the Kuramoto model incorporating a distribution of interaction delays. Corresponding to the case of a large number N of oscillators, we consider the continuum limit (i.e., N --> infinity). By focusing attention on the reduced dynamics on an invariant manifold of the original system, we derive governing equations for the system which we use to study the stability of the incoherent states and the dynamical transitional behavior from stable incoherent states to stable coherent states. We find that spread in the distribution function of delays can greatly alter the system dynamics.
133 citations
01 Jan 2009
TL;DR: Buchleitner and Tiersch as discussed by the authors introduced the theory of decoherence with an emphasis on its microscopic origins and on a dynamic description, which is the basis for our work.
Abstract: This is an introduction to the theory of decoherence with an emphasis on its microscopic origins and on a dynamic description. The text corresponds to a chapter soon to be published in: A. Buchleitner, C. Viviescas, and M. Tiersch (Eds.), Entanglement and Decoherence. Foundations and Modern Trends, Lecture Notes in Physics, Vol 768, Springer, Berlin (2009)
124 citations
TL;DR: In this paper, the authors give an explicit isomorphism between the usual spin network basis and the direct quantization of the reduced phase space of tetrahedra, and use their result to express the Freidel-Krasnov spin foam model as an integral over classical tetrahedral networks.
Abstract: In this work, we give an explicit isomorphism between the usual spin network basis and the direct quantization of the reduced phase space of tetrahedra. The main outcome is a formula that describes the space of SU(2) invariant states by an integral over coherent states satisfying the closure constraint exactly or, equivalently, as an integral over the space of classical tetrahedra. This provides an explicit realization of theorems by Guillemin–Sternberg and Hall that describe the commutation of quantization and reduction. In the final part of the paper, we use our result to express the Freidel–Krasnov spin foam model as an integral over classical tetrahedra, and the asymptotics of the vertex amplitude is determined.
107 citations
TL;DR: A multiple coherent states implementation of the semiclassical approximation is introduced and employed to obtain the power spectra with a few classical trajectories and successfully reproduce anharmonicity and Fermi resonance splittings at a level of accuracy comparable to semiclassicals simulations of thousands of trajectories.
Abstract: A multiple coherent states implementation of the semiclassical approximation is introduced and employed to obtain the power spectra with a few classical trajectories. The method is integrated with the time-averaging semiclassical initial value representation to successfully reproduce anharmonicity and Fermi resonance splittings at a level of accuracy comparable to semiclassical simulations of thousands of trajectories. The method is tested on two different model systems with analytical potentials and implemented in conjunction with the first-principles molecular dynamics scheme to obtain the power spectrum for the carbon dioxide molecule.
102 citations
TL;DR: In this paper, the authors give the optimal bounds on the phase estimation precision for mixed Gaussian states in the single-copy and many-copy regimes for displaced thermal and squeezed thermal states.
Abstract: We give the optimal bounds on the phase-estimation precision for mixed Gaussian states in the single-copy and many-copy regimes. Specifically, we focus on displaced thermal and squeezed thermal states. We find that while for displaced thermal states an increase in temperature reduces the estimation fidelity, for squeezed thermal states a larger temperature can enhance the estimation fidelity. The many-copy optimal bounds are compared with the minimum variance achieved by three important single-shot measurement strategies. We show that the single-copy canonical phase measurement does not always attain the optimal bounds in the many-copy scenario. Adaptive homodyning schemes do attain the bounds for displaced thermal states, but for squeezed states they yield fidelities that are insensitive to temperature variations and are, therefore, suboptimal. Finally, we find that heterodyne measurements perform very poorly for pure states but can attain the optimal bounds for sufficiently mixed states. We apply our results to investigate the influence of losses in an optical metrology experiment. In the presence of losses squeezed states cease to provide the Heisenberg limited precision, and their performance is close to that of coherent states with the same mean photon number.
TL;DR: In this paper, the authors show that there are effective three and higher-body interactions generated by the two-body collisions of atoms confined in the lowest vibrational states of a 3D optical lattice.
Abstract: We show that there are effective three- and higher-body interactions generated by the two-body collisions of atoms confined in the lowest vibrational states of a three-dimensional (3D) optical lattice. The collapse and revival dynamics of approximate coherent states loaded into a lattice are a particularly sensitive probe of these higher-body interactions; the visibility of interference fringes depend on both two-, three- and higher-body energy scales, and these produce an initial dephasing that can help explain the surprisingly rapid decay of revivals seen in experiments. If inhomogeneities in the lattice system are sufficiently reduced, longer timescale partial and nearly full revivals will be visible. Using Feshbach resonances or control of the lattice potential it is possible to tune the effective higher-body interactions and simulate effective field theories in optical lattices.
TL;DR: In this paper, the Schrodinger equation for a position-dependent mass quantum system is studied in two ways: first, the interaction is found which must be applied to a mass m(x) in order to supply it with a particular spectrum of energies.
Abstract: The solution of the Schrodinger equation for a position-dependent mass quantum system is studied in two ways. First, the interaction is found which must be applied to a mass m(x) in order to supply it with a particular spectrum of energies. Second, given a specific potential V(x) acting on the mass m(x), the related spectrum is found. The method of solution is applied to a wide class of position-dependent mass oscillators and the corresponding coherent states are constructed. The analytical expressions of such position-dependent mass coherent states preserve the functional structure of the Glauber states.
TL;DR: In this article, the authors investigated the properties of gauge-invariant coherent states for loop quantum gravity, for the gauge group U(1) by projecting the corresponding complexifier coherent states defined by Thiemann and Winkler to the gauge invariant Hilbert space.
Abstract: In this paper, we investigate the properties of gauge-invariant coherent states for loop quantum gravity, for the gauge group U(1). This is done by projecting the corresponding complexifier coherent states defined by Thiemann and Winkler to the gauge-invariant Hilbert space. This being the first step toward constructing physical coherent states, we arrive at a set of gauge-invariant states that approximate well the gauge-invariant degrees of freedom of Abelian loop quantum gravity (LQG). Furthermore, these states turn out to encode explicit information about the graph topology, and show the same pleasant peakedness properties known from the gauge-variant complexifier coherent states. In a companion paper, we will turn to the more sophisticated case of SU(2).
TL;DR: In this article, an explicit isomorphism between the usual spin network basis and the direct quantization of the reduced phase space of tetrahedra is given. But the main outcome is a formula that describes the space of SU(2) invariant states by an integral over coherent states satisfying the closure constraint exactly, or equivalently, as an integral of classical tetrahedral networks.
Abstract: In this work we give an explicit isomorphism between the usual spin network basis and the direct quantization of the reduced phase space of tetrahedra. The main outcome is a formula that describes the space of SU(2) invariant states by an integral over coherent states satisfying the closure constraint exactly, or equivalently, as an integral over the space of classical tetrahedra. This provides an explicit realization of theorems by Guillemin--Sternberg and Hall that describe the commutation of quantization and reduction. In the final part of the paper, we use our result to express the FK spin foam model as an integral over classical tetrahedra and the asymptotics of the vertex amplitude is determined.
TL;DR: In this paper, a quantum feedback scheme for the preparation and protection of photon-number states of light trapped in a high-Q microwave cavity is proposed, which is closed by injecting into the cavity a coherent pulse adjusted to increase the probability of the target photon number.
Abstract: We propose a quantum feedback scheme for the preparation and protection of photon-number states of light trapped in a high-Q microwave cavity. A quantum nondemolition measurement of the cavity field provides information on the photon-number distribution. The feedback loop is closed by injecting into the cavity a coherent pulse adjusted to increase the probability of the target photon number. The efficiency and reliability of the closed-loop state stabilization is assessed by quantum Monte Carlo simulations. We show that, in realistic experimental conditions, the Fock states are efficiently produced and protected against decoherence.
TL;DR: The number-conserving quantum phase space description of the Bose-Hubbard model is discussed in this article for the illustrative case of two and three modes, as well as the generalization of the two-mode case to an open quantum system.
Abstract: The number-conserving quantum phase space description of the Bose-Hubbard model is discussed for the illustrative case of two and three modes, as well as the generalization of the two-mode case to an open quantum system The phase-space description based on generalized $\mathrm{SU}(M)$ coherent states yields a Liouvillian flow in the macroscopic limit, which can be efficiently simulated using Monte Carlo methods even for large systems We show that this description clearly goes beyond the common mean-field limit In particular it resolves well-known problems where the common mean-field approach fails, such as the description of dynamical instabilities and chaotic dynamics Moreover, it provides a valuable tool for a semiclassical approximation of many interesting quantities, which depend on higher moments of the quantum state and are therefore not accessible within the common approach As a prominent example, we analyze the depletion and heating of the condensate A comparison to methods ignoring the fixed particle number shows that in this case artificial number fluctuations lead to ambiguities and large deviations even for quite simple examples
TL;DR: In this paper, the authors optimize two-mode entangled number states of light in the presence of photon loss in order to maximize the Fisher information, which is equivalent to minimizing the phase uncertainty.
Abstract: We optimize two-mode entangled number states of light in the presence of loss in order to maximize the extraction of the available phase information in an interferometer. Our approach optimizes over the entire available input Hilbert space with no constraints, other than fixed total initial photon number. We optimize to maximize the Fisher information, which is equivalent to minimizing the phase uncertainty. We find that in the limit of zero loss, the optimal state is the maximally path-entangled so-called N00N state, for small loss, the optimal state gradually deviates from the N00N state, and in the limit of large loss, the optimal state converges to a generalized two-mode coherent state, with a finite total number of photons. The results provide a general protocol for optimizing the performance of a quantum optical interferometer in the presence of photon loss, with applications to quantum imaging, metrology, sensing, and information processing.
TL;DR: In this paper, the authors present general formulas concerning supersymmetric quantum mechanics of first and second order for one-dimensional arbitrary systems, and illustrate the method through the trigonometric Poschl-Teller potentials.
Abstract: Supersymmetric quantum mechanics (SUSY QM) is a powerful tool for generating new potentials with known spectra departing from an initial solvable one. In these lecture notes we will present some general formulas concerning SUSY QM of first and second order for one-dimensional arbitrary systems, and we will illustrate the method through the trigonometric Poschl-Teller potentials. Some intrinsically related subjects, as the algebraic structure inherited by the new Hamiltonians and the corresponding coherent states will be analyzed. The technique will be as well implemented for periodic potentials, for which the corresponding spectrum is composed of allowed bands separated by energy gaps.
TL;DR: In this article, the Schrodinger equation with an exact time dependence is derived as eigenfunctions of dynamical invariants which are constructed from time-independent operators using time-dependent unitary transformations.
Abstract: Solutions of the Schrodinger equation with an exact time dependence are derived as eigenfunctions of dynamical invariants which are constructed from time-independent operators using time-dependent unitary transformations. Exact solutions and a closed form expression for the corresponding time evolution operator are found for a wide range of time-dependent Hamiltonians in d dimensions, including non-Hermitean -symmetric Hamiltonians. Hamiltonians are constructed using time-dependent unitary spatial transformations comprising dilatations, translations and rotations and solutions are found in several forms: as eigenfunctions of a quadratic invariant, as coherent state eigenfunctions of boson operators, as plane wave solutions from which the general solution is obtained as an integral transform by means of the Fourier transform, and as distributional solutions for which the initial wavefunction is the Dirac δ-function. For the isotropic harmonic oscillator in d dimensions radial solutions are found which extend known results for d = 1, including Barut–Girardello and Perelomov coherent states (i.e., vector coherent states), which are shown to be related to eigenfunctions of the quadratic invariant by the ζ-transformation. This transformation, which leaves the Ermakov equation invariant, implements SU(1, 1) transformations on linear dynamical invariants. coherent states are derived also for the time-dependent linear potential. Exact solutions are found for Hamiltonians with electromagnetic interactions in which the time-dependent magnetic and electric fields are not necessarily spatially uniform. As an example, it is shown how to find exact solutions of the time-dependent Schrodinger equation for the Dirac magnetic monopole in the presence of time-dependent magnetic and electric fields of a specified form.
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TL;DR: In this paper, it was shown that for free quantized Klein-Gordon and Dirac fields, this problem is solved very naturally in complex spacetime, where $|f(x-iy)|^2$ is interpreted as a probability density on all 6D phase spaces in T which, when integrated over the "momentum" variables y, gives a conserved spacetime probability current whose time component is a positive regularization of the usual one.
Abstract: The positivity of the energy in relativistic quantum mechanics implies that wave functions can be continued analytically to the forward tube T in complex spacetime. For Klein-Gordon particles, we interpret T as an extended (8D) classical phase space containing all 6D classical phase spaces as symplectic submanifolds. The evaluation maps $e_z: f\to f(z)$ of wave functions on T are relativistic coherent states reducing to the Gaussian coherent states in the nonrelativistic limit. It is known that no covariant probability interpretation exists for Klein-Gordon particles in real spacetime because the time component of the conserved "probability current" can attain negative values even for positive-energy solutions. We show that this problem is solved very naturally in complex spacetime, where $|f(x-iy)|^2$ is interpreted as a probability density on all 6D phase spaces in T which, when integrated over the "momentum" variables y, gives a conserved spacetime probability current whose time component is a positive regularization of the usual one. Similar results are obtained for Dirac particles, where the evaluation maps $e_z$ are spinor-valued relativistic coherent states. For free quantized Klein-Gordon and Dirac fields, the above formalism extends to n-particle/antiparticle coherent states whose scalar products are Wightman functions. The 2-point function plays the role of a reproducing kernel for the one-particle and antiparticle subspaces.
TL;DR: In this article, a simple scheme using two identical cross-phase modulation processes in decoherence environment to generate superpositions of two coherent states with the opposite phases, which are known as cat states, is presented.
Abstract: Department of Physics, Quaid-i-Azam University, Islamabad 45320, Pakistan(Dated: February 21, 2009)We present a simple scheme using two identical cross-phase modulation processes in decoherenceenvironment to generate superpositions of two coherent states with the opposite phases, which areknown as cat states. The scheme is shown to be robust against decoherence due to photon absorptionlosses and other errors, and the design of its experimental setup is also discussed.
TL;DR: In this article, it was shown that the spectrum of a cyclotron in a constant magnetic field has infinite degenerate Landau levels and that the position of the center of the circle plays the role of a Runge-Lenz vector.
TL;DR: Complete characterization of an optical memory based on electromagnetically induced transparency is reported and the acquired superoperator is employed to verify the nonclassicality benchmark for the storage of a Gaussian distributed set of coherent states.
Abstract: We report complete characterization of an optical memory based on electromagnetically induced transparency. We recover the superoperator associated with the memory, under two different working conditions, by means of a quantum process tomography technique that involves storage of coherent states and their characterization upon retrieval. In this way, we can predict the quantum state retrieved from the memory for any input, for example, the squeezed vacuum or the Fock state. We employ the acquired superoperator to verify the nonclassicality benchmark for the storage of a Gaussian distributed set of coherent states.
TL;DR: It is shown that a functional representation of self-similarity (as the one occurring in fractals) is provided by squeezed coherent states and the dissipative model of brain is shown to account for the self-Similarity in brain background activity suggested by power-law distributions of power spectral densities of electrocorticograms.
Abstract: I show that a functional representation of self-similarity (as the one occurring in fractals) is provided by squeezed coherent states. In this way, the dissipative model of brain is shown to account for the self-similarity in brain background activity suggested by power-law distributions of power spectral densities of electrocorticograms. I also briefly discuss the action-perception cycle in the dissipative model with reference to intentionality in terms of trajectories in the memory state space.
TL;DR: In this article, the Schrodinger equation for a position-dependent mass quantum system is studied in two ways: first, it is found the interaction which must be applied on a mass m(x) in order to supply it with a particular spectrum of energies.
Abstract: The solving of the Schrodinger equation for a position-dependent mass quantum system is studied in two ways. First, it is found the interaction which must be applied on a mass m(x) in order to supply it with a particular spectrum of energies. Second, given a specific potential V(x) acting on the mass m(x), the related spectrum is found. The method of solution is applied to a wide class of position-dependent mass oscillators and the corresponding coherent states are constructed. The analytical expressions of such position-dependent mass coherent states preserve the functional structure of the Glauber states.
TL;DR: In this paper, the Wigner function of quantum states in the entangled state representation is evaluated, based on which a new approach for deriving time evolution formula of Wigneer function in laser process is presented, where the initial state is a photon-added coherent state.
TL;DR: In this paper, the authors developed the fractional generalization of Bell polynomials, Bell numbers, and Stirling numbers of the second kind, and applied them to evaluate the skewness and kurtosis of fractional Poisson probability distribution.
Abstract: Physical and mathematical applications of the recently invented fractional Poisson probability distribution have been presented. As a physical application, a new family of quantum coherent states has been introduced and studied. As mathematical applications, we have developed the fractional generalization of Bell polynomials, Bell numbers, and Stirling numbers of the second kind. The appearance of fractional Bell polynomials is natural if one evaluates the diagonal matrix element of the evolution operator in the basis of newly introduced quantum coherent states. Fractional Stirling numbers of the second kind have been introduced and applied to evaluate the skewness and kurtosis of the fractional Poisson probability distribution function. A representation of the Bernoulli numbers in terms of fractional Stirling numbers of the second kind has been found. In the limit case when the fractional Poisson probability distribution becomes the Poisson probability distribution, all of the above listed developments and implementations turn into the well-known results of the quantum optics and the theory of combinatorial numbers.
TL;DR: In this article, a photon-added classical (coherent or thermal) state exhibits generalized nonclassical features in all orders of creation and annihilation operators, thereby becoming a promising candidate for studying higher-order non-classical effects.
Abstract: Detecting nonclassical properties that do not allow classical interpretation of photoelectric counting events is one of the crucial themes in quantum optics. Observation of individual nonclassical effects for a single-mode field, however, has been so far practically confined to sub-Poissonian statistics and quadrature squeezing. We show that a photon-added classical (coherent or thermal) state exhibits generalized nonclassical features in all orders of creation and annihilation operators, thereby becoming a promising candidate for studying higher-order nonclassical effects. Our analysis demonstrates the robustness of these effects against nonideal experimental conditions.
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TL;DR: In this article, a functional representation of self-similarity (as the one occurring in fractals) is provided by squeezed coherent states, and the dissipative model of brain is shown to account for the selfsimilarity in brain background activity suggested by power-law distributions of power spectral densities of electrocorticograms.
Abstract: I show that a functional representation of self-similarity (as the one occurring in fractals) is provided by squeezed coherent states. In this way, the dissipative model of brain is shown to account for the self-similarity in brain background activity suggested by power-law distributions of power spectral densities of electrocorticograms. I also briefly discuss the action-perception cycle in the dissipative model with reference to intentionality in terms of trajectories in the memory state space.