Preparation and decoherence of superpositions of electromagnetic field states

In a recent experiment the progressive decoherence of a mesoscopic superposition of two coherent field states in a high-Q cavity, known as Schr?dinger cat state, has been measured for the first time [Brune et al., Phys. Rev. Lett. 77, 4887 (1996)]. Here, the full master equation governing the coupled dissipative dynamics of the atom-field system studied in the experiment is formulated and solved numerically for the experimental parameters. The model simulated avoids the approximations underlying an analytically solvable model which is based on a harmonic expansion of the energies of the dressed atomic states and on a treatment of their dynamics within the adiabatic approximation. In particular, the numerical simulations reveal that the coupling of the cavity field mode to its environment causes important decoherence effects already during the initial preparation phase of the Schr?dinger cat state. This phenomenon is investigated in detail with the help of a measure for the purity of states. Moreover, the Hilbert-Schmidt distance of the intended target state, the Schr?dinger cat, to the state that is actually prepared in the experiment is determined. Received 13 September 2000 and Received in final form 22 December 2000     

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     

Localization of a macroscopic object induced by the factorization of internal adiabatic motion

To account for the phenomenon of quantum decoherence of a macroscopic object, such as the localization and disappearance of interference, we invoke the adiabatic quantum entanglement between its collective states (such as that of the center-of-mass (CM)) and its inner states based on our recent investigation. Under the adiabatic limit where motion of the CM does not excite the transition of inner states, it is shown that the wave function of the macroscopic object can be written as an entangled state with correlation between adiabatic inner states and quasi-classical motion configurations of the CM. Since the adiabatic inner states are factorized with respect to each component of the macroscopic object, this adiabatic separation can induce the quantum decoherence. This observation thus provides us with a possible solution to the Schr?dinger cat paradox. Received 24 October 2000 and Received in final form 8 March 2001     

Generation of motional cat states for a trapped ion in a cavity

Beyond the Lamb－Dicke limit, we propose a simple scheme for generating Schr?dinger cat states of the motion of a trapped two-level ion interacting with a quantized light field in a single-mode cavity.     

Implementing the Deutsch-Jozsa algorithm by using Schrodinger cat states in cavity QED

We propose a scheme to implement the Deutsch-Jozsa algorithm by using Schroedinger cat states in cavity quantum electron-dynamics （QED）. The scheme is based on the Raman interaction of a degenerate three-level A-type atom with a coherent state in a cavity. By using Schroedinger cat states, the atomic spontaneous emission can be minimized and the Hadamard transformation in our scheme is not needed.     

Monte Carlo wavefunction approach to the dissipative quantum-phase dynamics of two-component Bose-Einstein condensates

We investigate the relaxation effects on the dynamics of two-component dilute gas Bose-Einstein condensates (BEC) with relatively different two-body interactions and Josephson couplings between the two components. Three types of relaxation effects, i.e., one- and three-body losses and a pure phase relaxation caused by elastic two-body collision between condensed and noncondensed atoms, are examined on the dynamical behavior of a macroscopic superposition, i.e., Schr?dinger cat state, of two states with atom-number differences between the two components, which is known to be created by the time evolution in certain parameter regimes. Although three-body losses show a relatively large suppression of the revival behavior of Schr?dinger cat state and the Pegg-Barnett phase-difference distribution between the two components for a small-size Schr?dinger cat state, one- and three-body loss effects are not shown to directly depend on the size of Schr?dinger cat state. In contrast, the pure-phase relaxation effects, causing a reduction of phase-difference distribution and then decaying the Schr?dinger cat state, significantly increase with the increase of the size of Schr?dinger cat state. These features suggest that a detection of damped collapse-revival behavior is highly possible for medium-size Schr?dinger cat states in small-size two-component BECs.     

Generation of nonclassical states in a large detuning cavity

By using the theory of cavity QED, we study the system in which a two-level atom interacts with a cavity in the case of large detuning. Through the selective detecting of atomic state, Schrodinger cat states and entangled coherent states are easily generated. When the atom is driven by a weak classical field and the cavity field is in the Schrodinger cat state, we study the conditions of generating the Fock states and the maximal success probability. The maximal success probability in our scheme is larger than the previous one.     

利用介观LC电路制备薛定谔猫态

提出了一种制备相干态的叠加态，即薛定谔猫态的方案. 该方案是基于将外加冲激信号作用于介观LC电路系统而设计的. 在该薛定谔猫态下，介观电路系统有非经典的量子压缩效应. 关键词： 介观LC电路 冲激信号 薛定谔猫态     

Multi-component structure of nonlinear excitations in systems with length-scale competition

We investigate the properties of nonlinear excitations in different types of soliton carrying systems with long-range dispersive interactions. We show that length-scale competition in such systems, universally results in a multi-component structure of nonlinear excitations which may lead to a new type of multistability: coexistence of different nonlinear excitations at the same value of the spectral parameter (i.e., velocity in the case of anharmonic lattices or frequency in nonlinear Schr?dinger models). Received 31 August 2000 and Received in final form 14 December 2000     

PREPARATION OF NONCLASSICAL STATES OF A CAVITY FIELD BASED ON A NONLINEAR JAYNES-CUMMINGS MODEL

It is proven in this paper that some kinds of nonclassical quantum states of the cavity field, such as Schr?dinger cat state (amplitude cat or phase cat), sub-Poissonian photon distribution and Fock state, etc., can be generated by conditional meas urements on atoms in the two-photon Jaynes-Cummings model with a Kerr-like medium. The nonlinear constant plays the key modulation role in the preparation of the quantum states, which gives a new controllable parameter for further experi mental researches in this field.     

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     

Orienting molecules using half-cycle pulses

Using a rigid-rotor model, we study the orientation dynamics of polar diatomic molecules excited by experimentally available half-cycle pulses. The results of the numerical solution of the time-dependent Schr?dinger equation are compared to those of an approximate “sudden-impact” impulsive model neglecting the molecular rotation during the pulse. We show that efficient orientation is achieved during time periods of several picoseconds for LiCl. For short pulses, where the kicked molecule model is valid, orientation turns out to be mainly sensitive to the time-integrated field amplitude and not the shape or rise time of the pulse. Received 16 August 2000 and Received in final form 4 December 2000     

Engineering entanglement of a general three-level system interacting with a correlated two-mode nonlinear coherent state

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. Received 29 July 2002 / Received in final form 18 October 2002 Published online 21 January 2003 RID="a" ID="a"e-mail: abdelaty@uni-flensburg.dePresent address: Institut für Mathematik, Universit?t Flensburg, Germany.     

The dynamics of a THz Rydberg wavepacket

An optically excited Rydberg wavepacket can be generated by exciting the electron from a low-lying state to a coherent superposition of high-lying states with a short broadband optical pulse. A special kind of Rydberg wavepacket is generated in the case of a interaction of a weak THz half cycle pulse with a stationary Rydberg state, called the THz wavepacket. This THz wavepacket is a coherent superposition of the initial Rydberg state and its neighbouring states. We have investigated the time evolution of THz wavepackets by measuring the impact of two in time delayed half cycle pulses ( ≈ 200 V cm^-1) on the population of a stationary (n = 40) Rydberg state in rubidium. The first half cycle pulse creates the THz wavepacket and the second half cycle pulse probes the dynamics of the THz wavepacket. We support our experimental data by numerically solving the Schr?dinger equation and with a semi-classical picture. Whereas an optically excited wavepacket is initially localized, a THz wavepacket is initially delocalized and becomes localized after half a revival time. Received 23 August 2000 and Received in final form 27 March 2001     

利用微脉塞重构腔场的Wigner函数

提出了重构腔场Wigner函数的一种新方案.该方案可以用微脉塞来实现.发现在腔场的Wigner函数与原子的布居数之间存在一个简单的关系.在实验上测得原子的布居数后，进行一个简单的数值积分，就可得到腔场的Wigner函数.以单光子Fock态和Schr?dinger猫态为例进行了数值模拟，发现与用精确公式计算的结果很好地相符. 关键词： 量子态重构 Wigner函数 微脉塞     

Superpositions and Entanglement of Mesoscopic High-order Squeezed Vacuum States in Cavity QED

We propose a scheme for generating the superpositions and the entanglement between the mesoscopic high-order squeezed vacuum states by considering the multi-photon interaction of N two-level atoms in a cavity with high quality factor, assisted by a strong driving field. In terms of specific choices of the cavity detuning, many multiparty entangled states between the atoms and the mesoscopic high-order squeezed vacuum states and among the high-order squeezed vacuum states of the cavity modes can be generated, including the macroscopic “Schr?dinger cats” of the mesoscopic high-order squeezed vacuum states, the entanged states of the macroscopic “Schr?dinger cats”, and so on. Our scheme is achievable within the current techniques in the cavity QED.     

Interaction of coupled higher order nonlinear Schrödinger equation solitons

The novel inelastic collision properties of two-soliton interaction for an n-component coupled higher order nonlinear Schr?dinger equation are studied. Some interesting features of three soliton interactions, related to the integrability of the n-component coupled higher order nonlinear Schr?dinger equation are also discussed. Received 17 April 2002 Published online 2 October 2002 RID="a" ID="a"e-mail: abhijit@iitg.ernet.in RID="b" ID="b"e-mail: sasanka@iitg.ernet.in RID="c" ID="c"e-mail: sudipta@iitg.ernet.in     

Exciton-polariton solitary waves

Effects of the exciton and polariton dispersions and the nonlinear exciton and photon interactions on the properties of polariton solitons in molecular crystals are investigated. Higher-order terms and phase-modulation (chirp) are taken into account. Bright- and dark-soliton solutions of the resulting modified nonlinear Schr?dinger (NLS) equation are presented. Nonlinearity- and dispersion-induced critical points on the polariton dispersion curve are obtained, separating regions with different solutions. Received 2 October 2001 / Received in final form 23 May 2002 Published online 2 October 2002 RID="a" ID="a"e-mail: Stoychev@issp.bas.bg     

Next-nearest neighbor interaction and localized solutions of polymer chains

We study localization in polymer chains modeled by the nonlinear discrete Schr?dinger equation (DNLS) with next-nearest-neighbor (n-n-n) interaction extending beyond the usual nearest-neighbor exchange approximation. Modulational instability of plane carrier waves is discussed and it is shown that localization gets amplified under the influence of an enhanced interaction radius. Furthermore, we construct exact localized solitonlike solutions of the n-n-n interaction DNLS. To this end the stationary lattice system is cast into a nonlinear map. The homoclinic orbits of unstable equilibria of this map are attributed to standing solitonlike solutions of the lattice system. We note that in comparison with the standard next-neighbor interaction DNLS which bears only one type of static soliton-like states (either staggering or unstaggering) the one with n-n-n interaction radius can support unstaggering as well as staggering stationary localized states with frequencies lying above respectively below the linear band. Generally, the stronger the n-n-n interaction on the DNLS lattice the smaller are the maximal amplitudes of the standing solitonlike solutions and the less rapid are their exponential decays. Received 4 October 2000