Showing papers on "Coherent states in mathematical physics published in 2007"
TL;DR: In this paper, the authors discuss the spectral structure and decomposition of multi-photon states, and introduce an occupation number representation that provides an elegant description of such states, allowing to work in bases imposed by experimental constraints.
Abstract: We discuss the spectral structure and decomposition of multi-photon states. Ordinarily 'multi-photon states' and 'Fock states' are regarded as synonymous. However, when the spectral degrees of freedom are included this is not the case, and the class of 'multi-photon' states is much broader than the class of 'Fock' states. We discuss the criteria for a state to be considered a Fock state. We then address the decomposition of general multi-photon states into bases of orthogonal eigenmodes, building on existing multi-mode theory, and introduce an occupation number representation that provides an elegant description of such states. This representation allows us to work in bases imposed by experimental constraints, simplifying calculations in many situations. Finally we apply this technique to several example situations, which are highly relevant for state of the art experiments. These include Hong–Ou–Mandel interference, spectral filtering, finite bandwidth photo-detection, homodyne detection and the conditional preparation of Schrodinger kitten and Fock states. Our techniques allow for very simple descriptions of each of these examples.
93 citations
TL;DR: In this article, the authors discuss the role of coherent states in quantum nonlocality using the so-called mode entanglement, analyzing the differences between different types of particles in this context.
Abstract: We discuss the possibility of observing quantum nonlocality using the so-called mode entanglement, analyzing the differences between different types of particles in this context. We first discuss the role of coherent states in such experiments, and we comment on the existence of coherent states in nature. The discussion of coherent states naturally raises questions about the role of particle statistics in this problem. Although the Pauli exclusion principle precludes coherent states with a large number of fermionic particles, we find that a large number of fermionic coherent states, each containing at most one particle, can be used to achieve the same effect as a bosonic coherent state for the purposes of this problem. The discussion of superselection rules arises naturally in this context, because their applicability to a given situation prohibits the use of coherent states. This limitation particularly affects the scenario that we propose for detecting the mode entanglement of fermionic particles.
30 citations
TL;DR: In this paper, the Kratzer-Fues potential is constructed using the algebraic approach, which is important in the theory of molecular interactions with coherent electromagnetic fields, for example, in calculation of the dynamic alternation of the refractive index due to the interactions of the laser pulse with the coherent vibration-rotational states of the diatomic molecule.
Abstract: The coherent states for the Kratzer-Fues potential, which are eigenstates of the annihilation operator and minimize the generalized position-momentum uncertainty relation, are constructed using the algebraic approach. The method is extended to include the rotating Kratzer-Fues oscillator. Construction of such states is important in the theory of molecular interactions with coherent electromagnetic fields, for example, in calculation of the dynamic alternation of the refractive index due to the interactions of the laser pulse with the coherent vibration-rotational states of the diatomic molecule.
28 citations
TL;DR: In this paper, a nonlocal method for generating entangled coherent states of a two-mode field wherein the field modes never meet was proposed, which can be alternatively viewed as a ''which path'' experiment, and in the case of only one external field, the implementation of a quantum eraser was described.
Abstract: We describe a nonlocal method for generating entangled coherent states of a two-mode field wherein the field modes never meet. The proposed method is an extension of an earlier proposal [C. C. Gerry, Phys. Rev. A 59, 4095 (1999)] for the generation of superpositions of coherent states. A single photon injected into a Mach-Zehnder interferometer with cross-Kerr media in both arms coupling with two external fields in coherent states produces entangled coherent states upon detection at one of the output ports. We point out that our proposal can be alternatively viewed as a ``which path'' experiment, and in the case of only one external field, we describe the implementation of a quantum eraser.
26 citations
TL;DR: In this paper, the authors investigated the SU(1,1) Lie algebra for the time-dependent quadratic Hamiltonian system and derived exact wave functions for the system.
Abstract: Exact quantum states of the time-dependent quadratic Hamiltonian system are investigated using SU(1,1) Lie algebra. We realized SU(1,1) Lie algebra by defining appropriate SU(1,1) generators and derived exact wave functions using this algebra for the system. Raising and lowering operators of SU(1,1) Lie algebra expressed by multiplying a time-constant magnitude and a time-dependent phase factor. Two kinds of the SU(1,1) coherent states, i.e., even and odd coherent states and Perelomov coherent states are studied. We applied our result to the Caldirola–Kanai oscillator. The probability density of these coherent states for the Caldirola–Kanai oscillator converged to the center as time goes by, due to the damping constant γ. All the coherent state probability densities for the driven system are somewhat deformed.
22 citations
TL;DR: In this paper, the authors investigated the connection between quasi-classical (pointer) states and generalized coherent states (GCSs) within an algebraic approach to Markovian quantum systems (including bosons, spins, and fermions).
Abstract: We investigate the connection between quasi-classical (pointer) states and generalized coherent states (GCSs) within an algebraic approach to Markovian quantum systems (including bosons, spins, and fermions). We establish conditions for the GCS set to become most robust by relating the rate of purity loss to an invariant measure of uncertainty derived from quantum Fisher information. We find that, for damped bosonic modes, the stability of canonical coherent states is confirmed in a variety of scenarios, while for systems described by (compact) Lie algebras, stringent symmetry constraints must be obeyed for the GCS set to be preferred. The relationship between GCSs, minimum-uncertainty states, and decoherence-free subspaces is also elucidated.
21 citations
TL;DR: The coherent states for the quantum mechanics on a torus and their basic properties are discussed in this article, where the coherent states are defined as a set of coherent states of the quantum system on the torus.
Abstract: The coherent states for the quantum mechanics on a torus and their basic properties are discussed
20 citations
TL;DR: In this article, generalized and Gaussian coherent states constructed for quantum systems with degeneracies in the energy spectrum are compared with respect to some minimal definitions and fundamental properties they have to satisfy.
Abstract: Generalized and Gaussian coherent states constructed for quantum system with degeneracies in the energy spectrum are compared with respect to some minimal definitions and fundamental properties they have to satisfy. The generalized coherent states must be eigenstates of a certain annihilation operator that has to be properly defined in the presence of degeneracies. The Gaussian coherent states are, in the particular harmonic oscillator case, an approximation of the generalized coherent states and so the localizability in phase space of the particle in those states is very good. For other quantum systems, this last property serves as a definition of those Gaussian coherent states. The example of a particle in a two-dimensional square box is thus revisited having in mind the preceding definitions of generalized and Gaussian coherent states and also the preservation of the important property known as the resolution of the identity operator.
19 citations
01 Jan 2007
TL;DR: In this paper, the Schrodinger cat states (superpositions of well-separated coherent states) can be used for quantum information processing, and they are shown to be useful for quantum computing.
Abstract: In this chapter, we discuss how Schrodinger cat states (superpositions of well-separated coherent states) can be used for quantum information processing
17 citations
TL;DR: In this paper, a deformed harmonic oscillator algebra is used to construct a quantum field theory in confined space, and a physical scheme is proposed to generate the nonlinear coherent states associated with the electromagnetic field in a confined region.
Abstract: We study some basic quantum confinement effects through investigation a deformed harmonic oscillator algebra. We show that spatial confinement effects on a quantum harmonic oscillator can be represented by a deformation function within the framework of nonlinear coherent states theory. Using the deformed algebra, we construct a quantum field theory in confined space. In particular, we find that the confinement influences on some physical properties of the electromagnetic field and it gives rise to nonlinear interaction. Furthermore, we propose a physical scheme to generate the nonlinear coherent states associated with the electromagnetic field in a confined region.
13 citations
TL;DR: In this paper, a Fock space is introduced that admits an action of a quantum group of type A supplemented with some extra operators, and the canonical and dual canonical basis of the Fock spaces are computed and then used to derive the finite-dimensional tilting and irreducible characters for the Lie superalgebra osp(2|2n).
Abstract: A Fock space is introduced that admits an action of a quantum group of type A supplemented with some extra operators. The canonical and dual canonical basis of the Fock space are computed and then used to derive the finite-dimensional tilting and irreducible characters for the Lie superalgebra osp(2|2n). We also determine all the composition factors of the symmetric tensors of the natural osp(2|2n)-module.
TL;DR: In this paper, a straightening-free algorithm for computing the canonical bases of any higher-level q-deformed Fock space is presented, where the bases can be computed in any higher level.
TL;DR: In this paper, families of Perelomov coherent states are defined axiomatically in the context of unitary representations of Hopf algebras, and a global geometric picture involving locally trivial noncommutative fibre bundles is involved in the construction.
Abstract: Families of Perelomov coherent states are defined axiomatically in the context of unitary representations of Hopf algebras. A global geometric picture involving locally trivial noncommutative fibre bundles is involved in the construction. If, in addition, the Hopf algebra has a left Haar integral, then a formula for noncommutative resolution of identity in terms of the family of coherent states holds. Examples come from quantum groups.
TL;DR: In this paper, the authors discuss some basic tools for an analysis of one-dimensional quantum systems defined on a cyclic coordinate space, and use the complexifier coherent states for a semiclassical analysis.
Abstract: We discuss some basic tools for an analysis of one-dimensional quantum systems defined on a cyclic coordinate space. The basic features of the generalized coherent states, the complexifier coherent states, are reviewed. These states are then used to define the corresponding (quasi)densities in phase space. The properties of these generalized Husimi distributions are discussed, in particular their zeros. Furthermore, the use of the complexifier coherent states for a semiclassical analysis is demonstrated by deriving a semiclassical coherent state propagator in phase space.
TL;DR: In this paper, the coherent states for a particle in the Smorodinsky-Winternitz potentials were constructed in two coordinate frames and in four ocillators with the reflection symmetry.
Abstract: In this study, we construct the coherent states for a particle in the Smorodinsky-Winternitz potentials, which are the generalizations of the two-dimensional Kepler problem. In the third case, the system is transformed into four ocillators and the parametric-time coherent states are constructed in two coordinate frames. In the fourth case, the system is transformed into two ocillators with the reflection symmetry and the parametric-time coherent states are constructed in two coordinate frames.
TL;DR: In this article, the authors construct representations of the Lie algebra su (1, 1) using representations of momentum and position operators satisfying the R-deformed Heisenberg relations, in which the fractional dimension d and angular momentum l appear as parameters.
Abstract: We construct representations of the Lie algebra su (1, 1) using representations of the momentum and position operators satisfying the R-deformed Heisenberg relations, in which the fractional dimension d and angular momentum l appear as parameters. The Bargmann index K, which characterizes representations of the positive discrete series of su (1, 1), can take any positive value. We construct coherent states in fractional dimensions, in particular we extend the two well-known analytic representations of coherent states for su (1, 1), Perelomov and Barut-Girardello states, from dimension one to any dimension d. We generalize this construction to time-dependent coherent states by means of the su (1, 1) symmetries of the quantum time-dependent harmonic oscillator in fractional dimensions. We investigate the uncertainty relations of the momentum and position operators with respect to these coherent states, and their dependence on the dimension.
TL;DR: In this article, a generalized oscillator that is related to a system of orthogonal polynomials on the real axis was constructed, and coherent states in the Fock space associated with it were defined.
Abstract: We construct a system (a generalized oscillator) that is similar to the oscillator and is related to a system of orthogonal polynomials on the real axis. We define coherent states in the Fock space associated with the generalized oscillator. In the example of the generalized oscillator related to the Gegenbauer polynomials, we prove the (super)completeness of these coherent states, i.e., we construct a measure determining a partition of unity. We present a formula that allows calculating the Mandel parameter for the constructed coherent states.
TL;DR: In this article, two new types of quantum states are constructed by applying the operator s(ξ) = exp (ξ*ab−ξa†b†) on the two-mode even and odd coherent states.
Abstract: Two new types of quantum states are constructed by applying the operator s(ξ) = exp (ξ*ab−ξa†b†) on the two-mode even and odd coherent states. The mathematical and quantum statistical properties of such states are investigated. Various nonclassical features of these states, such as squeezing properties, the inter-mode photon bunching, and the violation of Cauchy–Schwarz inequality, are discussed. The Wigner function in these states are studied in detail.
Posted Content•
TL;DR: In this article, the effects of mode mismatching and loss in the preparation of large optical cat states are considered. But the authors focus on the effect of mode mismatch and loss on the performance of the protocol.
Abstract: A cat state is a superposition of macroscopically distinct states. In quantum optics one such type of state is a superposition of distinct coherent states. Recently, a protocol has been proposed for preparing large optical cat states from a resource of smaller ones. We consider the effects of mode-mismatch and loss in the preparation of large cat states using this protocol with a view to understand experimental limitations. (This paper is written in an experimental rapid communication format).
Posted Content•
TL;DR: In the realm of a quantum cosmological model for dark energy, a consistent coherent state representation has been formulated that may describe the quantum state of the universe and has a well-behaved semiclassical limit as mentioned in this paper.
Abstract: (Dated: February 2, 2008)In the realm of a quantum cosmological model for dark energy in which we have been able toconstruct a well-defined Hilbert space, a consistent coherent state representation has been formulatedthat may describe the quantum state of the universe and has a well-behaved semiclassical limit.
TL;DR: In this article, the authors introduced coherent mixed states (or thermal coherent states) associated with the displaced harmonic oscillator at nonzero temperature (T ≠ 0), as a "random" (or "thermal" or "noisy") basis in Hilbert space.
Abstract: We introduce coherent mixed states (or thermal coherent states) associated with the displaced harmonic oscillator at nonzero temperature (T ≠ 0), as a "random" (or "thermal" or "noisy") basis in Hilbert space. A resolution of the identity for these states is proven and is used to generalize the usual pure (T = 0) coherent state formalism to the mixed (T ≠ 0) case. This new formalism for thermal coherent states is then further generalized to a broader class of so-called negative-binomial mixed states. It is known that the negative-binomial distribution is itself intimately related to the discrete series of SU(1,1) representations. We consider the pure SU(1,1) coherent states in the two-mode harmonic oscillator space, and show how our negative-binomial mixed states arise from taking the partial trace with respect to one of these two modes. This observation is then used to show how the formalism of thermo-field dynamics may be generalized to a correspondingly much broader negative-binomial-field dynamics, which we expect to have many uses.
01 Jan 2007
TL;DR: In this paper, a simple scheme for computing phase space entropy measures for quantum systems treated within the Wigner function formalism is proposed, which is applied to eigenstates and coherent states of harmonic oscillator, and to the quantum optical "Schroedinger cat" states.
Abstract: A simple scheme is proposed for computing phase space entropy measures for quantum systems treated within the Wigner function formalism. The approach is applied to eigenstates and coherent states of harmonic oscillator, and to the quantum optical "Schroedinger cat" states. Along with the phase space representation, the Fock space (energetic) representation is invoked for the same problems. The essentially different behaviour of quantum entropies in the two mentioned representations is analysed.
Journal Article•
TL;DR: It is shown that the two mixed symmetric coherent states never give an eavesdropper more information than two pure coherent states.
Abstract: We use the probability of error as a measure of distinguishability between two pure and two mixed symmetric coherent states in the context of continuous variable quantum cryptography We show that the two mixed symmetric coherent states (in which the various components have the same real part) never give an eavesdropper more information than two pure coherent states
26 Aug 2007
TL;DR: In this paper, the eigenstate of a Hermitian operator related to the quantum Stokes operator was found for the measurement of three-photon states, where the two-polarization-mode Fock states were constructed from the two photon states and achieved Heisenberg-limited sensitivity in polarimetric measurements.
Abstract: Appropriate non-classical photon states, constructed from the two-polarization-mode Fock states, can attain Heisenberg-limited sensitivity in polarimetric measurements. We show that these states can be found as the eigenstates of a Hermitian operator related to the quantum Stokes operators, and provide a particular example of the measurement with the three-photon states.
13 Jun 2007
TL;DR: In this article, the authors provide experimental proposals for coherent communication with linear optics, including a linear-optical scheme for coherent superdense coding and a linearoptical coherent teleportation scheme.
Abstract: We provide experimental proposals for coherent communication with linear optics. The first proposal suggests a linear-optical scheme for coherent superdense coding. The second proposal gives a linear-optical coherent teleportation scheme.
16 Nov 2007
TL;DR: In this paper, the relation between the curvature of the physical space and the deformation function of the deformed oscillator algebra was investigated using a nonlinear coherent states approach, where the curvatures of the space and deformation functions were modeled as coherent states.
Abstract: In this paper, we investigate the relation between the curvature of the physical space and the deformation function of the deformed oscillator algebra using a non‐linear coherent states approach.