Monte Carlo Wave-function Approach Research Articles

Coherently Driven Micromaser Pumped by Atoms in Superposition States

Abstract By a Monte Carlo wave function approach we describe the dynamics of a coherently driven micromaser pumped by coherently prepared atoms. The system can exhibit nonclassical effects such as quadrature squeezing, sub-Poissonian photonstatistics, and Rabi oscillations revival. The interplay between driving field and polarised atoms allows manipulating both the photon number and the phase of the cavity field. By varying either the atomic transit time or the injected field intensity, the coherence of the system dynamics can be enhanced or even suppressed, whereas the induced cavity field phase can be shifted.

Dynamics of a coherently driven micromaser by the Monte Carlo wavefunction approach

Using a Monte Carlo wavefunction approach we investigate the dynamics of a micromaser driven by a resonant coherent field. At steady state, for increasing interaction times, the system exhibits driven Rabi oscillations, followed by collapse as the range of micromaser trapping states is approached. The system operates in regimes ranging from a strong to a weak amplifier. In the strong-amplifier regime the cavity mode shows a preferred phase and can exhibit quadrature squeezing and sub-Poissonian photon statistics. In the weak-amplifier regime the cavity mode has no preferred phase, is super-Poissonian and is influenced by trapping effects; no revival of Rabi oscillations occurs. The main predictions can be compared with experimental measurements on the populations of atoms leaving the cavity.

Comment on “Resonance fluorescence near a photonic band edge: Dressed-state Monte Carlo wave-function approach”

Quang and John have, in a recent paper [Phys. Rev. A $56,$ 4273 (1997)], proposed a dressed-state Monte Carlo wave-function (MCWF) approach to a laser-driven two-level atom coupled to a structured radiation reservoir. In this Comment, we argue that this approach is at variance with the underlying physical idea of the MCWF technique, that it is at variance with basic formal requirements for the MCWF technique to apply, and that it produces spurious and unphysical quantitative results for wide ranges of parameters.

Stochastic Schrödinger equations in cavity QED: physical interpretation and localization

We propose physical interpretations for stochastic methods which have been developed recently to describe the evolution of a quantum system interacting with a reservoir. As opposed to the usual reduced density operator approach, which refers to ensemble averages, these methods deal with the dynamics of single realizations, and involve the solution of stochastic Schr\"odinger equations. These procedures have been shown to be completely equivalent to the master equation approach when ensemble averages are taken over many realizations. We show that these techniques are not only convenient mathematical tools for dissipative systems, but may actually correspond to concrete physical processes, for any temperature of the reservoir. We consider a mode of the electromagnetic field in a cavity interacting with a beam of two- or three-level atoms, the field mode playing the role of a small system and the atomic beam standing for a reservoir at finite temperature, the interaction between them being given by the Jaynes-Cummings model. We show that the evolution of the field states, under continuous monitoring of the state of the atoms which leave the cavity, can be described in terms of either the Monte Carlo Wave-Function (quantum jump) method or a stochastic Schr\"odinger equation, depending on the system configuration. We also show that the Monte Carlo Wave-Function approach leads, for finite temperatures, to localization into jumping Fock states, while the diffusion equation method leads to localization into states with a diffusing average photon number, which for sufficiently small temperatures are close approximations to mildly squeezed states.

Resonance fluorescence near a photonic band edge: Dressed-state Monte Carlo wave-function approach

We introduce a dressed-state Monte Carlo wave-function technique to describe resonance fluorescence in a broad class of non-Markovian reservoirs with strong atom-reservoir interaction. The method recaptures photon localization effects which are beyond the Born and Markovian approximations, and describes the influence of the driving field on the atom-reservoir interaction. Using this approach, we predict a number of fundamentally new features in resonance fluorescence near the edge of a photonic band gap. In particular, the atomic population exhibits inversion for moderate applied field intensity. For a low external field intensity, the atomic system retains a long-time memory of its initial state.

Effect of atom pairs on the vacuum trapping state in micromasers: A Monte Carlo wave-function approach.

We calculate the lifetime of the vacuum trapping state in a micromaser, using both the Monte Carlo wave-function method and an analytic approximation, and show it to be a rapidly changing function of the average number of atoms in the cavity, when this number is much smaller than one. Our method leads to a realistic simulation of experiments, allowing for different field profiles, temperatures, and atomic velocity spreads. \textcopyright{} 1996 The American Physical Society.

Stochastic dynamics and quantum measurement

A simple quantum network consisting of up to four SU(2)-nodes (spin- subsystems) is studied to model explicitly the dynamics of quantum measurement processes. The resulting stochastic dynamics is simulated by the Monte Carlo wavefunction approach (MCWA) extended to composite few-particle systems. It is shown that the main features of axiomatic measurement theory can be recovered within this model, e.g. the dynamical emergence of projections, the superposition of undecidable alternatives. Exploiting the superposition of undecidable paths it is shown that EPR and GHZ states can be prepared within these quantum networks as attractor states.

Many-body quantum Monte Carlo wave-function approach to the dissipative atom-field interaction.

We develop a many-body quantum Monte Carlo wave-function approach to analyze the dissipative interaction of ultracold free atoms with the radiation field reservoir. A Markovian master equation for the identical atoms that neglects the dipole-dipole interaction is derived within the framework of quantum field theory. The effective Hamiltonian obtained by a decomposition of the master equation explicitly depends on the quantum statistics.

Quantum Monte Carlo wave-function approach to dissipative processes in mesoscopic semiconductors

We extend the quantum Monte Carlo wave-function approach of quantum optics to analyze the dissipative electron-phonon interaction in semiconductors. The non-unitary time-evolution of a stochastic wave-function by an effective Hamiltonian is combined with continuous “gedanken measurements” of phonon emission events, to simulate the electron dynamics.

Quantum-nondemolition measurements using dissipative atom-field coupling: Monte Carlo wave-function approach.

A continuous quantum-nondemolition measurement scheme that is based on intensity dependent atomic scattering in three-state systems is analyzed. The proposed scheme measures the number of photons in an optical cavity mode by observing the scattering rate of the atomic medium. The time evolution of the coupled atom-field system is analyzed using the Monte Carlo wave-function approach. The wave-function collapse occurs continuously as a result of the presence or absence of scattering events at each time instant. It is shown that the measurement is logically reversible and the information contained in the premeasurement wave function is preserved during the measurement interaction.

Logical reversibility in quantum-nondemolition measurements.

We show that it is possible to make a logically reversible quantum-nondemolition measurement of an optical-field photon number, where the measurement preserves all the information contained in the premeasurement wave function. The nonunitary dynamics of the proposed scheme is analyzed using a Monte Carlo wave-function approach.

Monte Carlo wave-function method in quantum optics

We present a wave-function approach to the study of the evolution of a small system when it is coupled to a large reservoir. Fluctuations and dissipation originate in this approach from quantum jumps that occur randomly during the time evolution of the system. This approach can be applied to a wide class of relaxation operators in the Markovian regime, and it is equivalent to the standard master-equation approach. For systems with a number of states N much larger than unity this Monte Carlo wave-function approach can be less expensive in terms of calculation time than the master-equation treatment. Indeed, a wave function involves only N components, whereas a density matrix is described by N2 terms. We evaluate the gain in computing time that may be expected from such a formalism, and we discuss its applicability to several examples, with particular emphasis on a quantum description of laser cooling.