Showing papers on "Coherent states published in 2003"
TL;DR: In this paper, it was shown that quantum computation circuits using coherent states as the logical qubits can be constructed from simple linear networks, conditional photon measurements, and small coherent superposition resource states.
Abstract: We show that quantum computation circuits using coherent states as the logical qubits can be constructed from simple linear networks, conditional photon measurements, and "small" coherent superposition resource states.
623 citations
TL;DR: In this paper, a general unified approach for arranging quantum operators of optical fields into ordered products (normal ordering, antinormal ordering, Weyl ordering) by fashioning Dirac's symbolic method and representation theory is presented.
Abstract: We present a general unified approach for arranging quantum operators of optical fields into ordered products (normal ordering, antinormal ordering, Weyl ordering (or symmetric ordering)) by fashioning Dirac's symbolic method and representation theory. We propose the technique of integration within an ordered product (IWOP) of operators to realize our goal. The IWOP makes Dirac's representation theory and the symbolic method more transparent and consequently more easily understood. The beauty of Dirac's symbolic method is further revealed. Various applications of the IWOP technique, such as in developing the entangled state representation theory, nonlinear coherent state theory, Wigner function theory, etc, are presented.
306 citations
TL;DR: In this article, the authors considered unstable D0-branes of two-dimensional string theory, described by the boundary state of Zamolodchikov and Verlinde [36] multiplied by the Neumann boundary state for the time coordinate t. This coherent state agrees with the exponential of the closed string one-point function on a disk with Sen's marginal boundary interaction for t which describes D-brane decay.
Abstract: We consider unstable D0-branes of two dimensional string theory, described by the boundary state of Zamolodchikov and Zamolodchikov [36] multiplied by the Neumann boundary state for the time coordinate t. In the dual description in terms of the c = 1 matrix model, this D0-brane is described by a matrix eigenvalue on top of the upside down harmonic oscillator potential. As suggested by McGreevy and Verlinde [25], an eigenvalue rolling down the potential describes D-brane decay. As the eigenvalue moves down the potential to the asymptotic region it can be described as a free relativistic fermion. Bosonizing this fermion we get a description of the state in terms of a coherent state of the tachyon field in the asymptotic region, up to a non-local linear field redefinition by an energy-dependent phase. This coherent state agrees with the exponential of the closed string one-point function on a disk with Sen's marginal boundary interaction for t which describes D0-brane decay.
304 citations
13 Mar 2003
TL;DR: The history of nonclassical states in quantum physics can be found in this paper, where the authors present a brief review of the state of the art in Quantum Physics and Quantum Optics, from the Jaynes-Cummings Model to collective interactions.
Abstract: 'Nonclassical' States in Quantum Physics: Brief Historical Review. Squeezed States. Parametric Excitation and Generation of Nonclassical States in Linear Media. Even and Odd Coherent States and Tomographic Representation of Quantum Mechanics and Quantum Optics. The Binormial States of Light. Nonclassical States in Kerr Media. From the Jaynes-Cummings Model to Collective Interactions.
251 citations
TL;DR: In this article, the authors formulate Feynman path integral on a non-commutative plane using coherent states and show that the propagator for a free particle exhibits UV cut-off induced by the parameter of non commutativity.
Abstract: We formulate Feynman path integral on a non commutative plane using coherent states. The propagator for a free particle exhibits UV cut-off induced by the parameter of non commutativity.
241 citations
TL;DR: In this paper, the authors considered unstable D0-branes of two-dimensional string theory, described by the boundary state of Zamolodchikov and Verlinde [hep-th/0304224] multiplied by the Neumann boundary state for the time coordinate $t.
Abstract: We consider unstable D0-branes of two dimensional string theory, described by the boundary state of Zamolodchikov and Zamolodchikov [hep-th/0101152] multiplied by the Neumann boundary state for the time coordinate $t$. In the dual description in terms of the $c=1$ matrix model, this D0-brane is described by a matrix eigenvalue on top of the upside down harmonic oscillator potential. As suggested by McGreevy and Verlinde [hep-th/0304224], an eigenvalue rolling down the potential describes D-brane decay. As the eigenvalue moves down the potential to the asymptotic region it can be described as a free relativistic fermion. Bosonizing this fermion we get a description of the state in terms of a coherent state of the tachyon field in the asymptotic region, up to a non-local linear field redefinition by an energy-dependent phase. This coherent state agrees with the exponential of the closed string one-point function on a disk with Sen's marginal boundary interaction for $t$ which describes D0-brane decay.
239 citations
TL;DR: In this article, the teleportation fidelity for a real experimental system is calculated explicitly, including relevant imperfection factors such as propagation losses, detection inefficiencies, and phase fluctuations, and the inferred fidelity for input coherent states is F = 0.61±0.02, which when corrected for the efficiency of detection by the output observer, gives a fidelity of 0.62.
Abstract: We experimentally demonstrate quantum teleportation for continuous variables using squeezed-state entanglement. The teleportation fidelity for a real experimental system is calculated explicitly, including relevant imperfection factors such as propagation losses, detection inefficiencies, and phase fluctuations. The inferred fidelity for input coherent states is F = 0.61±0.02, which when corrected for the efficiency of detection by the output observer, gives a fidelity of 0.62. By contrast, the projected result based on the independently measured entanglement and efficiencies is 0.69. The teleportation protocol is explained in detail, including a discussion on discrepancy between experiment and theory, as well as on the limitations of the current apparatus.
212 citations
TL;DR: In this paper, a sequence of eigenfunctions of the "quantum Arnold's cat map" is constructed in the semiclassical limit, which is the sum of the normalized Lebesgue measure on the torus plus the normalized Dirac measure concentrated on any a priori given periodic orbit of the dynamics.
Abstract: In this paper we construct a sequence of eigenfunctions of the ``quantum Arnold's cat map'' that, in the semiclassical limit, shows a strong scarring phenomenon on the periodic orbits of the dynamics. More precisely, those states have a semiclassical limit measure that is the sum of 1/2 the normalized Lebesgue measure on the torus plus 1/2 the normalized Dirac measure concentrated on any a priori given periodic orbit of the dynamics. It is known (the Schnirelman theorem) that ``most'' sequences of eigenfunctions equidistribute on the torus. The sequences we construct therefore provide an example of an exception to this general rule. Our method of construction and proof exploits the existence of special values of ¯h for which the quantum period of the map is relatively ``short'', and a sharp control on the evolution of coherent states up to this time scale. We also provide a pointwise description of these states in phase space, which uncovers their ``hyperbolic'' structure in the vicinity of the fixed points and yields more precise localization estimates.
192 citations
TL;DR: Petrosyan and Kurizki as mentioned in this paper proposed a fully quantized model of a double-EIT scheme, based on nonlinear interaction via double EIT of two light fields (initially prepared in coherent states).
Abstract: The generation of an entangled coherent state is one of the most important ingredients of quantum information processing using coherent states. Recently, numerous schemes to achieve this task have been proposed. In order to generate travelling-wave entangled coherent states, cross-phase-modulation, optimized by optical Kerr effect enhancement in a dense medium in an electromagnetically induced transparency (EIT) regime, seems to be very promising. In this scenario, we propose a fully quantized model of a double-EIT scheme recently proposed [D. Petrosyan and G. Kurizki, Phys. Rev. A 65, 33 833 (2002)]: the quantization step is performed adopting a fully Hamiltonian approach. This allows us to write effective equations of motion for two interacting quantum fields of light that show how the dynamics of one field depends on the photon-number operator of the other. The preparation of a Schr\"odinger cat state, which is a superposition of two distinct coherent states, is briefly exposed. This is based on nonlinear interaction via double EIT of two light fields (initially prepared in coherent states) and on a detection step performed using a 50:50 beam splitter and two photodetectors. In order to show the entanglement of an entangled coherent state, we suggest to measure the joint quadrature variance of the field. We show that the entangled coherent states satisfy the sufficient condition for entanglement based on quadrature variance measurement. We also show how robust our scheme is against a low detection efficiency of homodyne detectors.
158 citations
TL;DR: In this paper, the authors studied the purity of Gaussian states of single-mode continuous variable systems and showed that the joint measurement of two conjugate quadratures is sufficient and sufficient to determine the purity at any time.
Abstract: We present a systematic study of the purity for Gaussian states of single-mode continuous variable systems. We prove the connection of purity to observable quantities for these states, and show that the joint measurement of two conjugate quadratures is necessary and sufficient to determine the purity at any time. The statistical reliability and the range of applicability of the proposed measurement scheme are tested by means of Monte Carlo simulated experiments. We then consider the dynamics of purity in noisy channels. We derive an evolution equation for the purity of general Gaussian states both in thermal and in squeezed thermal baths. We show that purity is maximized at any given time for an initial coherent state evolving in a thermal bath, or for an initial squeezed state evolving in a squeezed thermal bath whose asymptotic squeezing is orthogonal to that of the input state.
140 citations
TL;DR: In this paper, a relativized notion of purity emerges, showing that there is a close relationship between purity, coherence, and (non)entanglement, and they propose ways in which these may be generalized to the Lie-algebraic setting and, to a lesser extent, to the convex-cones setting.
Abstract: Unentangled pure states on a bipartite system are exactly the coherent states with respect to the group of local transformations. What aspects of the study of entanglement are applicable to generalized coherent states? Conversely, what can be learned about entanglement from the well-studied theory of coherent states? With these questions in mind, we characterize unentangled pure states as extremal states when considered as linear functionals on the local Lie algebra. As a result, a relativized notion of purity emerges, showing that there is a close relationship between purity, coherence, and (non)entanglement. To a large extent, these concepts can be defined and studied in the even more general setting of convex cones of states. Based on the idea that entanglement is relative, we suggest considering these notions in the context of partially ordered families of Lie algebras or convex cones, such as those that arise naturally for multipartite systems. The study of entanglement includes notions of local operations and, for information-theoretic purposes, entanglement measures and ways of scaling systems to enable asymptotic developments. We propose ways in which these may be generalized to the Lie-algebraic setting and, to a lesser extent, to the convex-cones setting. One of our motivations for this program is to understand the role of entanglementlike concepts in condensed matter. We discuss how our work provides tools for analyzing the correlations involved in quantum phase transitions and other aspects of condensed-matter systems.
TL;DR: In this article, a single photon entangled with the vacuum is used to teleport single-mode quantum states of light by means of the Bennett protocol, which results in the truncation of their Fock expansion to the first two terms.
Abstract: We employ the quantum state of a single photon entangled with the vacuum (|GROUPA|GROUPB − |GROUPA|GROUPB), generated by a photon incident upon a symmetric beam splitter, to teleport single-mode quantum states of light by means of the Bennett protocol. The teleportation of coherent states results in the truncation of their Fock expansion to the first two terms. We analyze the teleported ensembles by means of homodyne tomography and obtain fidelities of up to 99 per cent for low-source state amplitudes. This work is an experimental realization of the quantum scissors device proposed by Pegg, Phillips and Barnett (Phys. Rev. Lett., 81 (1998) 1604).
TL;DR: In this article, the authors present a method to generate continuous variable-type entangled states between photons and atoms in atomic Bose-Einstein condensate (BEC) systems with three internal states, a weak quantized probe laser, and a strong classical coupling laser.
Abstract: In this paper, we present a method to generate continuous-variable-type entangled states between photons and atoms in atomic Bose-Einstein condensate (BEC). The proposed method involves an atomic BEC with three internal states, a weak quantized probe laser, and a strong classical coupling laser, which form a three-level $\ensuremath{\Lambda}$-shaped BEC system. We consider a situation where the BEC is in electromagnetically induced transparency with the coupling laser being much stronger than the probe laser. In this case, the upper and intermediate levels are unpopulated, so that their adiabatic elimination enables an effective two-mode model involving only the atomic field at the lowest internal level and the quantized probe laser field. Atom-photon quantum entanglement is created through laser-atom and interatomic interactions, and two-photon detuning. We show how to generate atom-photon entangled coherent states and entangled states between photon (atom) coherent states and atom-(photon-) macroscopic quantum superposition (MQS) states, and between photon-MQS and atom-MQS states.
TL;DR: In this paper, a forward-backward semiclassical dynamics (FBSD) method is proposed for the calculation of velocity autocorrelation function of liquid para-hydrogen at several thermodynamic state points (between T=14'k and T=25'k).
Abstract: Forward–backward semiclassical dynamics (FBSD) methods are emerging as a practical way of simulating dynamical processes in large quantum systems. In this paper we develop a pair-product approximation to the coherent state density. This form is accurate at low temperatures, enhancing significantly the convergence of Monte Carlo methods and thus allowing the simulation of quantum fluids. The scheme is applied to the calculation of velocity autocorrelation function of liquid para-hydrogen at several thermodynamic state points (between T=14 K and T=25 K). The results of the forward–backward semiclassical method with the pair-product approximation to the coherent state density exhibit good agreement with experimental measurements and other theoretical calculations. These calculations demonstrate that the FBSD method, in conjunction with an accurate representation of the coherent state density, allows an accurate description of dynamical processes in condensed phase systems at low temperatures where quantum me...
Patent•
07 Jul 2003TL;DR: In this article, the authors proposed a quantum cryptographic scheme comprising at least one sending unit including a physical means of encoding and distributing a raw key in the quadrature components of quantum coherent states that are continuously modulated in phase and amplitude.
Abstract: One aspect of the present invention is related to a quantum cryptographic scheme comprising at least one sending unit including a physical means of encoding and distributing a raw key in the quadrature components of quantum coherent states that are continuously modulated in phase and amplitude, at least one receiving unit containing a physical means of performing homodyne detection of the quantum coherent states in order to measure the quadrature components of the states, a quantum channel for connecting the sending unit to the receiving unit, a two-way authenticated public channel for transmitting non-secret messages between the sending unit and the receiving unit, a quantum key distribution protocol ensuring that the information tapped by a potential eavesdropper can be estimated from the quantum channel parameters, and a direct or reverse reconciliation protocol that converts the raw continuous data into a common binary key.
TL;DR: It is shown that these measures of complexity can be divergent; however, their differences are free from these divergences, thus enabling them to be good candidates for the description of the extension and the shape of continuous distributions.
Abstract: We discuss some properties of the generalized entropies, called Renyi entropies, and their application to the case of continuous distributions. In particular, it is shown that these measures of complexity can be divergent; however, their differences are free from these divergences, thus enabling them to be good candidates for the description of the extension and the shape of continuous distributions. We apply this formalism to the projection of wave functions onto the coherent state basis, i.e., to the Husimi representation. We also show how the localization properties of the Husimi distribution on average can be reconstructed from its marginal distributions that are calculated in position and momentum space in the case when the phase space has no structure, i.e., no classical limit can be defined. Numerical simulations on a one-dimensional disordered system corroborate our expectations.
TL;DR: In this article, the authors investigate the generation of multipartite entangled state in a system of N quantum dots embedded in a microcavity and examine the emergence of genuine multiqubit entanglement by three different characterizations of entenglement.
Abstract: We investigate the generation of multipartite entangled state in a system of N quantum dots embedded in a microcavity and examine the emergence of genuine multipartite entanglement by three different characterizations of entanglement. At certain times of dynamical evolution one can generate multipartite entangled coherent exciton states or multiqubit W states by initially preparing the cavity field in a superposition of coherent states or the Fock state with one photon, respectively. Finally, we study environmental effects on multipartite entanglement generation and find that the decay rate for the entanglement is proportional to the number of excitons.
TL;DR: It is demonstrated that the tip-induced Stark shift does not affect the motion of the electrons parallel to the surface and the momentum resolved phase-relaxation time of the first image-potential state is determined from the quantum interference patterns in the local density of states at step edges.
Abstract: The quantum dynamics of the two-dimensional image-potential states in front of the Cu(100) surface is measured by scanning tunneling microscopy and spectroscopy. The dispersion relation and the momentum resolved phase-relaxation time of the first image-potential state are determined from the quantum interference patterns in the local density of states at step edges. It is demonstrated that the tip-induced Stark shift does not affect the motion of the electrons parallel to the surface.
TL;DR: In this article, an example of an interaction that produces an infinite amount of entanglement in an infinitely short time, but only a finite amount in longer times is given, where the interaction arises from a standard Kerr nonlinearity and a 50/50 beam splitter and the initial state is a coherent state.
Abstract: An example is given of an interaction that produces an infinite amount of entanglement in an infinitely short time, but only a finite amount in longer times. The interaction arises from a standard Kerr nonlinearity and a 50/50 beam splitter, and the initial state is a coherent state. For certain finite interaction times multidimensional generalizations of entangled coherent states are generated, for which we construct a teleportation protocol. Similarities between probabilistic teleportation and unambiguous state discrimination are pointed out.
TL;DR: In this paper, an extension of the classical orthogonal functions invariant to the quantum domain is presented, expressed in terms of the Hamiltonian, and unitary transformations which involve the auxiliary function of this quantum invariant are used to solve the timedependent Schrodinger equation for a harmonic oscillator with time-dependent parameter.
Abstract: An extension of the classical orthogonal functions invariant to the quantum domain is presented. This invariant is expressed in terms of the Hamiltonian. Unitary transformations which involve the auxiliary function of this quantum invariant are used to solve the time-dependent Schrodinger equation for a harmonic oscillator with time-dependent parameter. The solution thus obtained is in agreement with the results derived using other methods which invoke the Lewis invariant in their procedures.
TL;DR: It is shown that at a suitable propagation distance, a maximum entangled state is created with a single-photon wave-packet state that has 50% probability of being in each of two product-type Fock states.
Abstract: We propose a method to achieve quantum entanglement of two Fock states with perfectly efficient, ultraslow propagation enhanced four-wave mixing. A cold atomic medium is illuminated with a two-mode cw control laser to produce coherent mixtures of excited states. An ultraslowly propagating, single-photon quantum probe field completes the four-wave mixing with 100% photon flux conversion efficiency, creating a depth dependent entanglement of two Fock states. We show that at a suitable propagation distance, a maximum entangled state is created with a single-photon wave-packet state that has 50% probability of being in each of two product-type Fock states.
TL;DR: In this paper, generalized coherent states were presented for systems with one degree of freedom having discrete and/or continuous spectra, and extended to systems with several degrees of freedom, give some examples and apply the formalism to the model of two-dimensional fermion gas in a constant magnetic field.
Abstract: Generalized coherent states were presented recently for systems with one degree of freedom having discrete and/or continuous spectra. We extend that definition to systems with several degrees of freedom, give some examples and apply the formalism to the model of two-dimensional fermion gas in a constant magnetic field.
TL;DR: In this article, the authors studied the time evolution for the quantum harmonic oscillator subjected to a sudden change of frequency and proposed an approximate analytic solution to the time dependent Ermakov equation for a step function.
TL;DR: In this paper, a treatment of a three-level atom interacting with two modes of light in a cavity with arbitrary forms of nonlinearities of both the fields and the intensity-dependent atom-field coupling is presented.
Abstract: In this article a treatment of a three-level atom interacting with two modes of light in a cavity with arbitrary forms of nonlinearities of both the fields and the intensity-dependent atom-field coupling is presented. A factorization of the initial density operator is assumed, with the privileged field modes being in a pair-coherent state. We derive and illustrate an exact expression for the time evolution of the density operator, by means of which we identify and numerically demonstrate the region of parameters where significantly large entanglement can be obtained. We show that entanglement can be significantly influenced by different kinds of nonlinearities. The nonlinear medium yields the superstructure of atomic Rabi oscillation. We propose a generation of Bell-type states having a simple initial state preparation of the present system.
TL;DR: Maths-type q-deformed coherent states with q > 1 allow a resolution of unity in the form of an ordinary integral as discussed by the authors, and they are sub-Poissonian and squeezed.
TL;DR: In this article, the entangled coherent-state representation (ECS) was introduced for describing and analyzing quantum optics sources and detectors while respecting the photon-number superselection rule that is satisfied by all known quantum optics experiments.
Abstract: We introduce the entangled coherent-state representation, which provides a powerful technique for efficiently and elegantly describing and analyzing quantum optics sources and detectors while respecting the photon-number superselection rule that is satisfied by all known quantum optics experiments. We apply the entangled coherent-state representation to elucidate and resolve the long-standing puzzles of the coherence of a laser output field, interference between two number states, and dichotomous interpretations of quantum teleportation of coherent states.
TL;DR: In this paper, a Gaussian quantum operator representation of density matrices for Bose systems is presented. But the representation is not suitable for quantum many-body systems, and it is not a suitable representation for quantum quantum uncertainties.
Abstract: We introduce a Gaussian quantum operator representation, using the most general possible multimode Gaussian operator basis. The representation unifies and substantially extends existing phase-space representations of density matrices for Bose systems and also includes generalized squeezed-state and thermal bases. It enables first-principles dynamical or equilibrium calculations in quantum many-body systems, with quantum uncertainties appearing as dynamical objects. Any quadratic Liouville equation for the density operator results in a purely deterministic time evolution. Any cubic or quartic master equation can be treated using stochastic methods.
TL;DR: The coherent states of the Gompertzian systems, which minimize the time-energy uncertainty relation, have been found.
Abstract: The origin of the Gompertz function G(t)=G(0)e(b/a(1-e(-at))) widely applied to fit the biological and medical data, particularly growth of organisms, organs, and tumors is analyzed. It is shown that this function is a solution of a time-dependent counterpart of the Schrodinger equation for the Morse oscillator with anharmonicity constant equal to 1. The coherent states of the Gompertzian systems, which minimize the time-energy uncertainty relation, have been found. These are eigenstates of the annihilation operator identified with the operator of growth, whereas eigenstates of the creation operator represent the Gompertzian states of regression. The coherent formation of the specific growth patterns in the Gompertzian systems appears as a result of the nonlocal long-range cooperation between the microlevel (the individual cell) and the macrolevel (the system as a whole).
TL;DR: In this paper, the interaction of a three-level atom with a single mode field in a cavity containing a Kerr-like medium was studied and the wave function for the atomic system of V-configuration was obtained when the atom was initially prepared in the excited state.
TL;DR: In this article, an exactly solvable case of an interacting Hamiltonian of two bosonic modes is considered to study fundamental properties of the entanglement dynamics for coupled nonlinear oscillators.
Abstract: An exactly solvable case of an interacting Hamiltonian of two bosonic modes is considered to study fundamental properties of the entanglement dynamics for coupled nonlinear oscillators. Such an interaction is of physical importance, either in a two-species Bose–Einstein condensate or in the case of two modes of electromagnetic fields interacting in Kerr media. The time-evolved state is obtained analytically for initial products of two Fock and two coherent states, and the purification times of the subsystems are determined. The possibility of dynamical generation of a quantum superposition state is discussed at such purification times. We also identify the existence of two regimes: the short time, phase spread regime where subsystem entropy rises monotonically and the self-interference regime where it oscillates and a purification phenomenon can be observed. Our results also show that the break time from the first regime to the second one becomes longer, as well as the purification and reversibility times, as the Planck constant becomes much smaller than a typical action in phase space.