Quantum-information processing for a coherent superposition state via a mixed entangled coherent channel

An entangled two-mode coherent state is studied within the framework of 2 x 2-dimensional Hilbert space. An entanglement concentration scheme based on joint Bell-state measurements is worked out. When the entangled coherent state is embedded in vacuum environment, its entanglement is degraded but not totally lost. It is found that the larger the initial coherent amplitude, the faster entanglement decreases. We investigate a scheme to teleport a coherent superposition state while considering a mixed quantum channel. We find that the decohered entangled coherent state may be useless for quantum teleportation as it gives the optimal fidelity of teleportation less than the classical limit 2/3.

Representation and properties of para-Bose oscillator operators. II. Coherent states and the minimum uncertainty states

The energy, position, and momentum eigenstates of a para-Bose oscillator system were considered in paper I. Here we consider the Bargmann or the analytic function description of the para-Bose system. This brings in, in a natural way, the coherent states ||z;alpha> defined as the eigenstates of the annihilation operator ?. The transformation functions relating this description to the energy, position, and momentum eigenstates are explicitly obtained. Possible resolution of the identity operator using coherent states is examined. A particular resolution contains two integrals, one containing the diagonal basis ||z;alpha><−z;alpha||. We briefly consider the normal and antinormal ordering of the operators and their diagonal and discrete diagonal coherent state approximations. The problem of constructing states with a minimum value of the product of the position and momentum uncertainties and the possible alpha dependence of this minimum value is considered. Journal of Mathematical Physics is copyrighted by The American Institute of Physics.

Coherent classical-path description of deep tunneling

A central challenge to the semiclassical description of quantum mechanics is the quantum phenomenon of "deep" tunneling. Here we show that real time classical trajectories suffice to account correctly even for deep quantum tunneling, using a recently formulated semiclassical initial value representation series of the quantum propagator and a prefactor free semiclassical propagator. Deep quantum tunneling is effected through what we term as coherent classical paths which are composed of one or more classical trajectories that lead from reactant to product but are discontinuous along the way. The end and initial phase space points of consecutive classical trajectories contributing to the coherent path are close to each other in the sense that the distance between them is weighted by a coherent state overlap matrix element. Results are presented for thermal and energy dependent tunneling through a symmetric Eckart barrier.

Efficient quantum computation using coherent states

We study universal quantum computation using optical coherent states. A teleportation scheme for a coherent-state qubit is developed and applied to gate operations. This scheme is shown to be robust to detection inefficiency.

Conditional production of superpositions of coherent states with inefficient photon detection

It is shown that a linear superposition of two macroscopically distinguishable optical coherent states can be generated using a single photon source and simple all-optical operations. Weak squeezing on a single photon, beam mixing with an auxiliary coherent state, and photon detecting with imperfect threshold detectors are enough to generate a coherent state superposition in a free propagating optical field with a large coherent amplitude (alpha>2) and high fidelity (F>0.99). In contrast to all previous schemes to generate such a state, our scheme does not need photon number resolving measurements nor Kerr-type nonlinear interactions. Furthermore, it is robust to detection inefficiency and exhibits some resilience to photon production inefficiency.

Perspectives for quantum state engineering via high nonlinearity in a double-EIT regime

We analyse the possibilities for quantum state engineering offered by a model for Kerr-type nonlinearity enhanced by electromagnetically induced transparency (EIT), which was recently proposed by Petrosyan and Kurizki [2002, Phys. Rev. A, 65, 33833]. We go beyond the semiclassical treatment and derive a quantum version of the model with both a full Hamiltonian approach and an analysis in terms of dressed states. The preparation of an entangled coherent state via a cross-phase modulation effect is demonstrated. We briefly show that the violation of locality for such an entangled coherent state is robust against low detection efficiency. Finally, we investigate the possibility of a bi-chromatic photon blockade realized via the interaction of a low density beam of atoms with a bi-modal electromagnetic cavity which is externally driven. We show the effectiveness of the blockade effect even when more than a single atom is inside the cavity. The possibility to control two different cavity modes allows some insights into the generation of an entangled state of cavity modes.

Vibrational coherent quantum computation

A long-lived coherent state and nonlinear interaction have been experimentally demonstrated for the vibrational mode of a trapped ion. We propose an implementation of quantum computation using coherent states of the vibrational modes of trapped ions. Differently from earlier experiments, we consider a far-off resonance for the interaction between external fields and the ion in a bidimensional trap. By appropriate choices of the detunings between the external fields, the adiabatic elimination of the ionic excited level from the Hamiltonian of the system allows for beam splitting between orthogonal vibrational modes, production of coherent states, and nonlinear interactions of various kinds. In particular, this model enables the generation of the four coherent Bell states. Furthermore, all the necessary operations for quantum computation, such as preparation of qubits and one-qubit and controlled two-qubit operations, are possible. The detection of the state of a vibrational mode in a Bell state is made possible by the combination of resonant and off-resonant interactions between the ion and some external fields. We show that our read-out scheme provides highly efficient discrimination between all the four Bell states. We extend this to a quantum register composed of many individually trapped ions. In this case, operations on two remote qubits are possible through a cavity mode. We emphasize that our remote-qubit operation scheme does not require a high-quality factor resonator: the cavity field acts as a catalyst for the gate operation.

Generation of entangled coherent states via cross-phase-modulation in a double electromagnetically induced transparency regime

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 Schrodinger 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.

Discrete coherent states and probability distributions in finite-dimensional spaces

Operator bases are discussed in connection with the construction of phase space representatives of operators in finite-dimensional spaces, and their properties are presented. It is also shown how these operator bases allow for the construction of a finite harmonic oscillator-like coherent state. Creation and annihilation operators for the Fock finite-dimensional space are discussed and their expressions in terms of the operator bases are explicitly written. The relevant finite-dimensional probability distributions are obtained and their limiting behavior for an infinite-dimensional space are calculated which agree with the well known results. (C) 1996 Academic Press, Inc.

Spin coherent states in NMR quadrupolar system: experimental and theoretical applications

Working with nuclear magnetic resonance (NMR) in quadrupolar spin systems, in this paper we transfer the concept of atomic coherent state to the nuclear spin context, where it is referred to as pseudonuclear spin coherent state (pseudo-NSCS). Experimentally, we discuss the initialization of the pseudo- NSCSs and also their quantum control, implemented by polar and azimuthal rotations. Theoretically, we compute the geometric phases acquired by an initial pseudo-NSCS on undergoing three distinct cyclic evolutions: (i) the free evolution of the NMR quadrupolar system and, by analogy with the evolution of the NMR quadrupolar system, that of (ii) single-mode and (iii) two-mode Bose-Einstein Condensate like system. By means of these analogies, we derive, through spin angular momentum operators, results equivalent to those presented in the literature for orbital angular momentum operators. The pseudo-NSCS description is a starting point to introduce the spin squeezed state and quantum metrology into nuclear spin systems of liquid crystal or solid matter.

Conditional production of superpositions of coherent states with inefficient photon detection

It is shown that a linear superposition of two macroscopically distinguishable optical coherent states can be generated using a single photon source and simple all-optical operations. Weak squeezing on a single photon, beam mixing with an auxiliary coherent state, and photon detecting with imperfect threshold detectors are enough to generate a coherent state superposition in a free propagating optical field with a large coherent amplitude (alpha>2) and high fidelity (F>0.99). In contrast to all previous schemes to generate such a state, our scheme does not need photon number resolving measurements nor Kerr-type nonlinear interactions. Furthermore, it is robust to detection inefficiency and exhibits some resilience to photon production inefficiency.

Fock-state dynamics in Raman photoassociation of Bose-Einstein condensates

By stochastic modeling of the process of Raman photoassociation of Bose-Einstein condensates, we show that, the farther the initial quantum state is from a coherent state, the farther the one-dimensional predictions are from those of the commonly used zero-dimensional approach. We compare the dynamics of condensates, initially in different quantum states, finding that, even when the quantum prediction for an initial coherent state is relatively close to the Gross-Pitaevskii prediction, an initial Fock state gives qualitatively different predictions. We also show that this difference is not present in a single-mode type of model, but that the quantum statistics assume a more important role as the dimensionality of the model is increased. This contrasting behavior in different dimensions, well known with critical phenomena in statistical mechanics, makes itself plainly visible here in a mesoscopic system and is a strong demonstration of the need to consider physically realistic models of interacting condensates.

Production of superpositions of coherent states in traveling optical fields with inefficient photon detection

We develop an all-optical scheme to generate superpositions of macroscopically distinguishable coherent states in traveling optical fields. It nondeterministically distills coherent-state superpositions (CSS's) with large amplitudes out of CSS's with small amplitudes using inefficient photon detection. The small CSS's required to produce CSS's with larger amplitudes are extremely well approximated by squeezed single photons. We discuss some remarkable features of this scheme: it effectively purifies mixed initial states emitted from inefficient single-photon sources and boosts negativity of Wigner functions of quantum states.