Showing papers on "Coherent states in mathematical physics published in 2011"
TL;DR: An improved phase estimation scheme employing entangled coherent states is presented and it is demonstrated that these states give the smallest variance in the phase parameter in comparison to NOON, "bat," and "optimal" states under perfect and lossy conditions.
Abstract: We present an improved phase estimation scheme employing entangled coherent states and demonstrate that these states give the smallest variance in the phase parameter in comparison to NOON, ``bat,'' and ``optimal'' states under perfect and lossy conditions. As these advantages emerge for very modest particle numbers, the optical version of entangled coherent state metrology is achievable with current technology.
409 citations
TL;DR: This work presents a direct observation of a classical analogue for the emergence of coherent states from the eigenstates of the harmonic oscillator, and shows that the square-root distribution of the coupling parameter in such lattices supports a new family of intriguing quantum correlations not encountered in uniform arrays.
Abstract: Coherent states and their generalizations, displaced Fock states, are of fundamental importance to quantum optics. Here we present a direct observation of a classical analogue for the emergence of these states from the eigenstates of the harmonic oscillator. To this end, the light propagation in a Glauber-Fock waveguide lattice serves as equivalent for the displacement of Fock states in phase space. Theoretical calculations and analogue classical experiments show that the square-root distribution of the coupling parameter in such lattices supports a new family of intriguing quantum correlations not encountered in uniform arrays. Because of the broken shift invariance of the lattice, these correlations strongly depend on the transverse position. Consequently, quantum random walks with this extra degree of freedom may be realized in Glauber-Fock lattices.
95 citations
TL;DR: In this paper, a general formalism for the construction of deformed photon-added nonlinear coherent states (DPANCSs) |α, f, m, which in a special case lead to the well-known PACS|α, m.
Abstract: In this paper, we will try to present a general formalism for the construction of deformed photon-added nonlinear coherent states (DPANCSs) |α, f, m, which in a special case lead to the well-known photon-added coherent state (PACS) |α, m. Some algebraic structures of the introduced DPANCSs are studied and particularly the resolution of the identity, as the most important property of generalized coherent states, is investigated. Meanwhile, it will be demonstrated that the introduced states can also be classified in the f-deformed coherent states, with a special nonlinearity function. Next, we will show that these states can be produced through a simple theoretical scheme. A discussion on the DPANCSs with negative values of m, i.e. |α, f, −m, is then presented. Our approach has the potentiality to be used for the construction of a variety of new classes of DPANCSs, corresponding to any nonlinear oscillator with known nonlinearity function, as well as arbitrary solvable quantum system with known discrete, non-degenerate spectrum. Finally, after applying the formalism to a particular physical system known as the Poschl–Teller (P-T) potential and the nonlinear coherent states corresponding to a specific nonlinearity function , some of the non-classical properties, such as the Mandel parameter, second-order correlation function, in addition to first- and second-order squeezing of the corresponding states, will be investigated numerically.
55 citations
TL;DR: In this paper, the authors construct nonlinear coherent states for Hamiltonians with linear and quadratic terms in the number operator by the generalization of two definitions: as eigenstates of a deformed annihilation operator and as those states obtained by the application of deformed displacement operator on the vacuum state.
Abstract: In this work, we construct nonlinear coherent states for Hamiltonians with linear and quadratic terms in the number operator by the generalization of two definitions: as eigenstates of a deformed annihilation operator and as those states obtained by the application of a deformed displacement operator on the vacuum state. We evaluate their temporal dependence, analyze its dispersion relations and some of their statistical properties for two model Hamiltonians, one supporting a finite number of bound states and the other supporting an infinite number of bound states.
38 citations
TL;DR: In this article, the authors constructed coherent states for power-law potentials using generalized Heisenberg algebra and investigated the statistical properties of these states through the evaluation of the Mandel's parameter.
32 citations
TL;DR: In this paper, the maximum success probability of the circuits with passive linear optics for expanding an N-photon W state to an (N + n)-photon N state, by accessing only one photon of the initial W state and adding n photons in a Fock state, was derived.
Abstract: We derive the maximum success probability of the circuits with passive linear optics for expanding an N-photon W state to an (N + n)-photon W state, by accessing only one photon of the initial W state and adding n photons in a Fock state. We show that the maximum success probability is achieved by a polarization-dependent beamsplitter and n-1 polarization-independent beamsplitters.
29 citations
TL;DR: In this paper, a generalized deformation of the su(2) algebra and a scheme for constructing associated spin coherent states is developed, and the problem of resolving the unity operator in terms of these states is addressed and solved for some particular cases.
Abstract: A generalized deformation of the su(2) algebra and a scheme for constructing associated spin coherent states is developed. The problem of resolving the unity operator in terms of these states is addressed and solved for some particular cases. The construction is carried using a deformation of Holstein-Primakoff realization of the su(2) algebra. The physical properties of these states is studied through the calculation of Mandel’s parameter.
25 citations
TL;DR: The complex geometry underlying the Schrodinger dynamics of coherent states for non-Hermitian Hamiltonians is investigated in this article, where two seemingly contradictory approaches are compared: (i) a complex WKB formalism, for which the centres of coherent state naturally evolve along complex trajectories, which leads to a class of complexified coherent states; and (ii) the investigation of the dynamical equations for the real expectation values of position and momentum.
Abstract: The complex geometry underlying the Schrodinger dynamics of coherent states for non-Hermitian Hamiltonians is investigated. In particular two seemingly contradictory approaches are compared: (i) a complex WKB formalism, for which the centres of coherent states naturally evolve along complex trajectories, which leads to a class of complexified coherent states; (ii) the investigation of the dynamical equations for the real expectation values of position and momentum, for which an Ehrenfest theorem has been derived in a previous paper, yielding real but non-Hamiltonian classical dynamics on phase space for the real centres of coherent states. Both approaches become exact for quadratic Hamiltonians. The apparent contradiction is resolved building on an observation by Huber, Heller and Littlejohn, that complexified coherent states are equivalent if their centres lie on a specific complex Lagrangian manifold. A rich underlying complex symplectic geometry is unravelled. In particular a natural complex structure is identified that defines a projection from complex to real phase space, mapping complexified coherent states to their real equivalents.
25 citations
TL;DR: In this paper, a set of N-dimensional functions, based on generalized SU(N)-symmetric coherent states, that represent finite-dimensional Wigner functions, Q-functions, and P-function are presented.
Abstract: We present a set of N-dimensional functions, based on generalized SU(N)-symmetric coherent states, that represent finite-dimensional Wigner functions, Q-functions, and P-functions. We then show the fundamental properties of these functions and discuss their usefulness for analyzing N-dimensional pure and mixed quantum states.
22 citations
TL;DR: In this paper, a general approach for building coherent states associated to generalized su(1, 1) algebra is developed, and the problem of completeness of these coherent states is studied for some particular cases.
22 citations
TL;DR: In this article, generalized coherent states based on Gazeau-Klauder formalism are developed for one-dimensional power-law potentials and their quantum statistical characteristics, together with generalized Heisenberg algebra coherent states, are reported.
Abstract: Generalized coherent states based on Gazeau-Klauder formalism are developed for one-dimensional power-law potentials and their quantum statistical characteristics, together with generalized Heisenberg algebra coherent states, are reported. We show that these states exhibit super-Poissonian, Poissonian, or sub-Poissonian distributions as a function of the power-law exponent. The analytical results are supported by numerical calculations. In addition, we explain possible sources of errors in numerical analysis.
TL;DR: In this paper, the generalized coherent state for quantum systems with degenerate spectra is introduced and the nonclassicality features and number-phase entropic uncertainty relation of two particular degenerate quantum systems are studied.
Abstract: In this paper, the generalized coherent state for quantum systems with degenerate spectra is introduced. Then, the nonclassicality features and number-phase entropic uncertainty relation of two particular degenerate quantum systems are studied. Finally, using the Gazeau–Klauder coherent states approach, the time evolution of some of the nonclassical properties of the coherent states corresponding to the considered physical systems are discussed.
TL;DR: In this article, the authors proposed a scheme by which this projection can be engineered, which requires relatively weak cross-Kerr nonlinearities, the ability to perform a displacement operation on a beam mode, and photon detection ability able to distinguish between zero and any other number of photons.
Abstract: The pair coherent states of a two-mode quantized electromagnetic field introduced by Agarwal [Phys. Rev. Lett. 57, 827 (1986)] have yet to be generated in the laboratory. The states can mathematically be obtained from a product of ordinary coherent states via projection onto a subspace wherein identical photon number states of each mode are paired. We propose a scheme by which this projection can be engineered. The scheme requires relatively weak cross-Kerr nonlinearities, the ability to perform a displacement operation on a beam mode, and photon detection ability able to distinguish between zero and any other number of photons. These requirements can be fulfilled with currently available technology or technology that is on the horizon.
TL;DR: In this article, the problem of building coherent states from non-normalizable fiducial states is considered and a way of constructing such coherent states by regularizing the divergence of the fiducual state norm is proposed.
Abstract: The problem of building coherent states from non-normalizable fiducial states is considered. We propose a way of constructing such coherent states by regularizing the divergence of the fiducial state norm. Then, we successfully apply the formalism to particular cases involving systems with a continuous spectrum: coherent states for the free particle and for the inverted oscillator $(p^2 - x^2)$ are explicitly provided. Similar ideas can be used for other systems having non-normalizable fiducial states.
TL;DR: In this article, the authors derived coherent states of the Perelomov type for finite-dimensional representations of A(x) and A(s) through a Fock-Bargmann analytical approach based on the use of complex (or bosonic) variables.
Abstract: The aim of this article is to construct a la Perelomov and a la Barut-Girardello coherent states for a polynomial Weyl-Heisenberg algebra. This generalized Weyl-Heisenberg algebra, noted A(x), depends on r real parameters and is an extension of the one-parameter algebra introduced in Daoud M and Kibler MR 2010 J. Phys. A: Math. Theor. 43 115303 which covers the cases of the su(1,1) algebra (for x > 0), the su(2) algebra (for x < 0) and the h(4) ordinary Weyl-Heisenberg algebra (for x = 0). For finite-dimensional representations of A(x) and A(x,s), where A(x,s) is a truncation of order s of A(x) in the sense of Pegg-Barnett, a connection is established with k-fermionic algebras (or quon algebras). This connection makes it possible to use generalized Grassmann variables for constructing certain coherent states. Coherent states of the Perelomov type are derived for infinite-dimensional representations of A(x) and for finite-dimensional representations of A(x) and A(x,s) through a Fock-Bargmann analytical approach based on the use of complex (or bosonic) variables. The same approach is applied for deriving coherent states of the Barut-Girardello type in the case of infinite-dimensional representations of A(x). In contrast, the construction of a la Barut-Girardello coherent states for finite-dimensional representations of A(x) and A(x,s) can be achieved solely at the price to replace complex variables by generalized Grassmann (or k-fermionic) variables. Some of the results are applied to su(2), su(1,1) and the harmonic oscillator (in a truncated or not truncated form).
TL;DR: In this paper, a class of nonlinear coherent states related to the Susskind-Glogower (phase) operators is obtained, and the coefficients that expand them into number states are Bessel functions.
Abstract: A class of nonlinear coherent states related to the Susskind-Glogower (phase) operators is obtained. We call these nonlinear coherent states as Bessel states because the coefficients that expand them into number states are Bessel functions. We give a closed form for the displacement operator that produces such states.
TL;DR: In this article, it was shown that affine kinematical variables can serve equally well for many classical and quantum studies, such as quantization of non-renormalizable scalar quantum field theory by affine techniques, in contrast to canonical techniques which only offer triviality.
Abstract: Affine coherent states are generated by affine kinematical variables much like canonical coherent states are generated by canonical kinematical variables. Although all classical and quantum formalisms normally entail canonical variables, it is shown that affine variables can serve equally well for many classical and quantum studies. This general purpose analysis provides tools to discuss two major applications: (1) the completely successful quantization of a nonrenormalizable scalar quantum field theory by affine techniques, in complete contrast to canonical techniques which only offer triviality; and (2) a formulation of the kinematical portion of quantum gravity that favors affine kinematical variables over canonical kinematical variables, and which generates a framework in which a favorable analysis of the constrained dynamical issues can take place. All this is possible because of the close connection between the affine and the canonical stories, while the few distinctions can be used to advantage when appropriate.
TL;DR: In this paper, a q-deformed oscillator for pseudo-Hermitian systems is investigated and pseudo-hermitian appropriate coherent and squeezed states are studied, and some basic properties of these states are surveyed.
Abstract: In this paper, q-deformed oscillator for pseudo-Hermitian systems is investigated and pseudo-Hermitian appropriate coherent and squeezed states are studied. Also, some basic properties of these states is surveyed. The over-completeness property of the para- Grassmannian pseudo-Hermitian coherent states (PGPHCSs) examined, and also the stabili- ty of coherent and squeezed states discussed. The pseudo-Hermitian supercoherent states as the product of a pseudo-Hermitian bosonic coherent state and a para-Grassmannian pseudo- Hermitian coherent state introduced, and the method also developed to define pseudo- Hermitian supersqueezed states. It is also argued that, for q-oscillator algebra of k + 1 degree of nilpotency based on the changed ladder operators, defined in here, we can obtain deformed SUq2(2) and SUq2k(2) and also SUq2k(1; 1). Moreover, the entanglement of multi- level para-Grassmannian pseudo-Hermitian coherent state will be considered. This is done by choosing an appropriate weight function, and integrating over tensor product of PGPHCSs.
TL;DR: It is shown that Barut-Girardello coherent states are useful in describing the states of real and ideal lasers by a proper choice of their characterizing parameters, using an alteration of the Holstein-Primakoff realization.
Abstract: Using linear entropy as a measure of entanglement, we investigate the entanglement generated via a beam splitter using deformed Barut-Girardello coherent states. We show that the degree of entanglement depends strongly on the q-deformation parameter and amplitude Z of the states. We compute the Mandel Q parameter to examine the quantum statistical properties of these coherent states and make a comparison with the Glauber coherent states. It is shown that these states are useful in describing the states of real and ideal lasers by a proper choice of their characterizing parameters, using an alteration of the Holstein-Primakoff realization.
TL;DR: In this paper, the authors briefly review some applications of dynamical Lie algebras and groups and their associated coherent states in quantum optics and molecular spectroscopy, and present a survey of these applications.
Abstract: We briefly review some applications of dynamical Lie algebras and groups and their associated coherent states in quantum optics and molecular spectroscopy.
TL;DR: In this paper, a correspondence between positive operator valued measures (POVMs) and sets of generalized coherent states is presented, which leads to a useful characterization of extremal POVMs, and it is shown that covariant phase space observables related to squeezed states are extremal while the ones related to number states are not extremal.
Abstract: We present a correspondence between positive operator valued measures (POVMs) and sets of generalized coherent states. Positive operator valued measures describe quantum observables and, similarly to quantum states, also quantum observables can be mixed. We show how the formalism of generalized coherent states leads to a useful characterization of extremal POVMs. We prove that covariant phase space observables related to squeezed states are extremal, while the ones related to number states are not extremal.
TL;DR: In this article, two new possible hamiltonians are proposed, self-adjoint and positive, which also produce the same differential equation as the original Pais-Uhlenbeck model.
Abstract: In some recent papers many quantum aspects of the Pais-Uhlenbeck model were discussed. In particular, several inequivalent hamiltonians have been proposed, with different features, giving rise, at a quantum level, to the fourth-order differential equation of the model. Here we propose two new possible hamiltonians which also produce the same differential equation. In particular our first hamiltonian is self-adjoint and positive. Our second proposal is written in terms of pseudo-bosonic operators. We discuss in details the ground states of these hamiltonians and the (bi-)coherent states of the models.
TL;DR: In this article, a particle moving on a 2-sphere in the presence of a constant magnetic field is considered and coherent states are constructed as eigenvectors for certain annihilation operators and expressed in terms of a heat kernel.
Abstract: We consider a particle moving on a 2-sphere in the presence of a constant magnetic field. Building on earlier work in the nonmagnetic case, we construct coherent states for this system. The coherent states are labeled by points in the associated phase space, the (co)tangent bundle of S^2. They are constructed as eigenvectors for certain annihilation operators and expressed in terms of a certain heat kernel. These coherent states are not of Perelomov type, but rather are constructed according to the "complexifier" approach of T. Thiemann. We describe the Segal--Bargmann representation associated to the coherent states, which is equivalent to a resolution of the identity.
TL;DR: In this paper, a criterion of classicality for mixed states in terms of expectation values of a quantum observable is given, where the criterion can be computed exactly in the spectrum of a single operator.
Abstract: We give a criterion of classicality for mixed states in terms of expectation values of a quantum observable. Using group representation theory we identify all cases when the criterion can be computed exactly in terms of the spectrum of a single operator.
TL;DR: In this article, a comparative study of the down-conversion process and atom-cavity interaction in generating the photon-added coherent states is presented, and it is shown that the scheme can generate higher order photon-add coherent states.
Abstract: Photon-added coherent states have been realized in optical parametric down-conversion by Zavatta et al [Science 306 (2004) 660-662]. In this report, it is established that the states generated in the process are ideal photon-added coherent states. It is shown that the scheme can generate higher order photon-added coherent states. A comparative study of the down-conversion process and atom-cavity interaction in generating the photon-added coherent states is presented.
TL;DR: In this paper, light evolution occurring in waveguide arrays with a particular n-functional square root dependence of coupling coefficients can be used to produce classical analogues of nonlinear quantum coherent states.
01 Mar 2011
TL;DR: In this article, the authors present a possible construction of coherent states on the unit circle as configuration space, where the phase space is the product ×S 1 and the duality of canonical coordinates and momenta is exploited to construct coherent states over an infinite periodic chain.
Abstract: We present a possible construction of coherent states on the unit circle as configuration space. In our approach the phase space is the product ×S1. Because of the duality of canonical coordinates and momenta, i.e. the angular variable and the integers, this formulation can also be interpreted as coherent states over an infinite periodic chain. For the construction we use the analogy with our quantization over a finite periodic chain where the phase space was M ×M. Properties of the coherent states constructed in this way are studied and the coherent states are shown to satisfy the resolution of unity.
TL;DR: In this paper, it was shown that there is only one non-trivial Hilbert space of functions that is invariant under the action of a unitary representation of the Heisenberg group.
Abstract: We show that there is only one non-trivial Hilbert space of entire functions that is invariant under the action of a certain unitary representation of the Heisenberg group.
TL;DR: In this article, the main axioms of Gazeau-Klauder coherent states were shown to be satisfied properly and the introduced excited coherent states for continuous spectra were discussed.
Abstract: Based on the definition of coherent states for continuous spectra and analogous to photon-added coherent states for discrete spectra, we introduce the excited coherent states for continuous spectra. It is shown that the main axioms of Gazeau–Klauder coherent states will be satisfied, properly. Nonclassical properties and quantum statistics of coherent states, as well as the introduced excited coherent states, are discussed. In particular, through the study of quadrature squeezing and amplitude-squared squeezing, it will be observed that both classes of the above states can be classified in the intelligent states category.