Proposal for preparing entangled coherent states using atom-cavity-mode Raman interaction

A scheme for preparing entangled coherent states is presented. It is based on the atom-cavity-mode Raman interaction. We also generalize this method for generating multi-mode entangled coherent states. Finally, our experimental feasibility is discussed. Received 15 September 2001 and Received in final form 15 November 2001     

Quantum state engineering using conditional measurement on a beam splitter

State preparation via conditional output measurement on a beam splitter is studied, assuming the signal mode is mixed with a mode prepared in a Fock state and photon numbers are measured in one of the output channels. It is shown that the mode in the other output channel is prepared in either a photon-subtracted or a photon-added Jacobi polynomial state, depending upon the difference between the number of photons in the input Fock state and the number of photons in the output Fock state onto which it is projected. The properties of the conditional output states are studied for coherent and squeezed input states, and the probabilities of generating the states are calculated. Relations to other states, such as near-photon-number states and squeezed-state-excitations, are given and proposals are made for generating them by combining the scheme with others. Finally, effects of realistic photocounting and Fock-state preparation are discussed. Received: 17 March 1998 / Revised and Accepted: 8 May 1998     

EPR entangled states and complex fractional Fourier transformation

Starting from the Einstein-Podolsky-Rosen entangled state representations of continuous variables we derive a new formulation of complex fractional Fourier transformation (CFFT). We find that two-variable Hermite polynomials are just the eigenmodes of the CFFT. In this way the CFFT is linked to the appropriate operator transformation between two kinds of entangled states in the context of quantum mechanics. In so doing, the CFFT of quantum mechanical wave functions can be derived more directly and concisely. Received 21 February 2002 / Received in final form 1st June 2002 Published online 24 September 2002 RID="*" ID="*"Work supported by National Natural Science Foundation of China under grant 10175057 and the President Foundation of Chinese Academy of Science. RID="a" ID="a"e-mail: fhym@ustc.edu.cn     

Photon entanglement in the phase-space Q representation of quantum optics

Several examples of photon entanglement are studied in the Q representation of quantum optics. In particular, the entangled states produced in parametric downconversion are studied in detail, and we determine the conditions for the violation of Bell's inequality. Our approach shows that photon entanglement is related to the existence of correlations between the quantum fluctuations of the electromagnetic field associated to different modes. Received 10 August 2002 / Received in final form 7 November 2002 Published online 4 February 2003     

Triggered single photons and entangled photons from a quantum dot microcavity

Current quantum cryptography systems are limited by the attenuated coherent pulses they use as light sources: a security loophole is opened up by the possibility of multiple-photon pulses. By replacing the source with a single-photon emitter, transmission rates of secure information can be improved. We have investigated the use of single self-assembled InAs/GaAs quantum dots as such single-photon sources, and have seen a tenfold reduction in the multi-photon probability as compared to Poissonian pulses. An extension of our experiment should also allow for the generation of triggered, polarization-entangled photon pairs. The utility of these light sources is currently limited by the low efficiency with which photons are collected. However, by fabricating an optical microcavity containing a single quantum dot, the spontaneous emission rate into a single mode can be enhanced. Using this method, we have seen 78% coupling of single-dot radiation into a single cavity resonance. The enhanced spontaneous decay should also allow for higher photon pulse rates, up to about 3 GHz. Received 8 July 2001 and Received in final form 25 August 2001     

A single atom-based generation of Bell states of two cavities

A new conditional scheme for generating Bell states of two spatially separated high-Q cavities is reported. Our method is based on the passage of one atom only through the two cavities. A distinctive feature of our treatment is that it incorporates from the very beginning the unavoidable presence of fluctuations in the atom-cavity interaction times. The possibility of successfully implementing our proposal against cavity losses and atomic spontaneous decay is carefully discussed. Received 31 July 2001 and Received in final form 9 October 2001     

Generation of superpositions of coherent states on a circle

We propose a simple method to obtain a superposition of coherent states on a circle, including Schr?dinger cat states as a special case, via conditional measurement of the state of three level atoms interacting with a one mode cavity field. In the low amplitude limit, very good approximation of Fock states can also be generated in this way. Received: 8 October 1998 / Accepted: 30 October 1998     

Statistical properties of a solvable three-boson squeeze operator model

In the present paper we introduce a new squeeze operator, which is related to the time-dependent evolution operator for Hamiltonian representing mutual interaction between three different modes. Squeezing phenomenon as well as the variances of the photon-number sum and difference are considered. Moreover, Glauber second-order correlation function is discussed, besides the quasiprobability distribution function and phase distribution for different states. The joint photon-number distribution is also reported. Received 29 March 2000 and Received in final form 20 September 2000     

Steady-state populations of a driven three-level atom in a broad-band squeezed vacuum

A theoretical study is made of the steady-state populations of a three-level atom in a ladder configuration, driven by a superposition of a monochromatic laser wave with a broad-band squeezed vacuum. The master equation for the system and the atomic Bloch equations are derived. The steady-state populations are calculated numerically and shown graphically as functions of two-photon detuning for various cases of the squeezed vacuum. It is shown that, the atomic populations depend strongly on the relative phase of the driving field and the squeezed vacuum. When the phase matching condition is fulfilled, there will be a strong two-photon resonant absorption from the squeezed vacuum, a characteristic different from absorption of photons from a classical field. Received: 28 May 1997 / Revised and Accepted: 10 December 1997     

Twin photons entangled in polarization and angular momentum

Quantum states of twin photons entangled in angular momentum and polarization provide new degrees of freedom to researchers in quantum information and imaging. This work discuss these states and also emphasizes differences between two proposed models for twin photons entangled in angular momentum. Answers to the presented questions would contribute to a better understanding of this nonlinear process. Received 30 August 2002 / Received in final form 10 October 2002 Published online 21 January 2003     

Effective quantum efficiency in the pulsed homodyne detection of a n-photon state

Homodyne detection can be used to perform measurements on various quantum states of the light, such as conditional single photon states produced by parametric fluorescence processes. In the pulsed regime, the time and frequency overlap between the single photon wave packet and the local oscillator field plays a crucial role. We show in this paper that this overlap can be characterized by an effective quantum efficiency, which is explicitly calculated in various situations of experimental interest. Received 27 July 2000 and Received in final form 29 November 2000     

Quantum state transfer from light beams to atomic ensembles

We show the equivalence between an ensemble of two-level atoms driven by a squeezed vacuum field, and a harmonic oscillator coupled to a squeezed field. We give the conditions for optimal squeezing transfer from the field to the atomic ensemble. We show that EPR-type correlations are created between the atomic ensemble and the incoming field. Received 23 January 2001     

Interference and correlation of two independent photons

Two independent photons, produced through the spontaneous emission of two separate emitters subject to uncorrelated dephasing processes, can display two-photon interference (i.e. coalescence into a two-photon state) when they are incident simultaneously on a beamsplitter, in a manner analogous to that of twin photons produced through degenerate parametric fluorescence. The presence of dephasing processes, however, reduces the interference contrast (i.e. the probability of coalescence), by the ratio of the coherence time to the lifetime of the emitter. Received 9 September 2002 Published online 17 December 2002 RID="a" ID="a"e-mail: izo.abram@lpn.cnrs.fr     

Evolution of cat states in a dissipative parametric amplifier: decoherence and entanglement

The evolution of the Schr?dinger-cat states in a dissipative parametric amplifier is examined. The main tool in the analysis is the normally ordered characteristic function. Squeezing, photon-number distribution and reduced factorial moments are discussed for the single- and compound-mode cases. Also the single-mode Wigner function is demonstrated. In addition to the decoherence resulting from the interaction with the environment (damped case) there are two sources which can cause such decoherence in the system even if it is completely isolated: these are the decay of the pump and the relative phases of the initial cat states. Furthermore, for the damped case there are two regimes, which are underdamped and overdamped. In the first (second) regime the signal mode or the idler mode “collapses" to a statistical mixture (thermal field). Received 25 September 2001 / Received in final form 30 May 2002 Published online 13 December 2002 RID="a" ID="a"e-mail: sebaweh@awalnet.net.sa RID="b" ID="b"Joint Laboratory of Optics of Palacky University and Institute of Physics, Academy of Sciences of the Czech Republic, 17. listopadu 50, 772 07 Olomouc, Czech Republic.     

Eigenstates of boson creation operator

We examine the existence of right-hand eigenstates (or eigenkets) of the boson creation operator a and determine their coordinate and their Bargmann representation. The eigenkets of the creation operator are ultrasingular and cannot be considered as a limiting case of normalizable states. Applications of these eigenstates as auxiliary states for purposes of representation of states by path integrals over coherent states are discussed. A completeness relation for coherent states on paths through the complex plane is derived and special examples of its application are considered. Received 9 March 2001 and Received in final form 13 June 2001     

Preparation of Fock states and quantum entanglement via stimulated Raman adiabatic passage using a four-level atom

We study the behaviour of an atom-cavity system exposed to a stimulated Raman adiabatic passage (STIRAP) process in a four-level system, with a coupling scheme which generate two degenerate dark states. We find that the non-adiabatic interaction of the two dark states guarantees that the cavity Fock states can always be generated by both intuitively and counterintuitively ordered pulses. Furthermore, we propose a method to entangle two atoms. Depending on the ordering of the pulses two orthogonal entangled states can be prepared. Since these entangled states do not have component of the excited states included, the technique is robust against the detrimental consequences of spontaneous emission. Received 20 March 2001     

Bell inequalities for a sensible family of local hidden variable theories testable at low detection efficiency

A family of local models containing two angles as hidden variables is defined for experiments measuring polarization correlation of optical photons. Searching for the best model of the family, that is giving predictions most close to quantum mechanics, allows deriving Bell-type inequalities which may be tested with relatively low detection efficiency.     

Direct experimental test of non-separability and other quantum techniques using continuous variables of light

We present schemes for the generation and evaluation of continuous variable entanglement of bright optical beams and give a brief overview of a variety of optical techniques and quantum communication applications on this basis. A new entanglement-based quantum interferometry scheme with bright beams is suggested. The performance of the presented schemes is independent of the relative interference phase which is advantageous for quantum communication applications. Received 1st August 2001     

Series solution to the laser-ion interaction in a Raman-type configuration

The Raman interaction of a ultracold ion trapped with two travelling wave lasers is studied analytically with series solutions, in the absence of the rotating wave approximation (RWA) and without restrictions of both the Lamb-Dicke limit and the weak excitation regime. The comparison is made between our solutions and those obtained under the RWA in order to demonstrate the validity region of the RWA. As a practical example, the preparation of Schr?dinger-cat states is proposed beyond the weak excitation regime, using our calculations. Received 12 March 2001 and Received in final form 16 October 2001     

Atomic-dipole squeezing for arbitrarily prepared atom and field in multi-photon interaction

Summary The atomic-dipole squeezing condition for arbitrarily prepared atomic and field states in multi-photon Jaynes-Cummings model was derived. Three special cases were discussed. For the field initially in a vacuum state and a certain eigenstate of the Susskind-Glogower phase operator, the analytical dipole squeezing conditions were obtained and the maximum squeezing values were calculated. For a squeezed vacuum input field, the dipole squeezing behaviours under the influence of the field squeezing parameterr and the phased atom were numerically treated.