Europhysics Letters (EPL)

Non-Markovian spectral broadening in interacting continuous-wave atom lasers

Heinz‐Peter Breuer, Daniel Faller, Bernd Kappler, Francesco Petruccione

Published Apr 1, 2001• 11 citations

Abstract

The non-Markovian dynamics of a continuous-wave atom laser model is studied which includes gravitational effects and interactions inside the Bose-Einstein condensate. With the help of the time-convolutionless projection operator technique both the occupation number of the condensate and the spectrum of the atoms coupled out of the condensate are determined. A correct modeling of memory effects in the atom laser requires a generalization of the projection operator technique which takes into account correlations in the initial state of the combined atom-reservoir system. The non-Markovian evolution is shown to yield substantial deviations from results obtained in the Born-Markov approximation.

DOI: 10.1209/epl/i2001-00222-0

Related papers

Non-Markovian dynamics in pulsed- and continuous-wave atom lasers

Heinz‐Peter Breuer, Daniel Faller, Bernd Kappler +1 more

The dynamics of atom lasers with a continuous output coupler based on two-photon Raman transitions is investigated. With the help of the time-convolutionless projection operator technique the quantum master equations for pulsed- and continuous-wave (cw) atom lasers are derived. In the case of the pulsed atom laser the power of the time-convolutionless projection operator technique is demonstrated through comparison with the exact solution. It is shown that in an intermediate coupling regime where the Born-Markov approximation fails, the results of this algorithm agree with the exact solution. To study the dynamics of a continuous-wave atom laser a pump mechanism is included in the model. Whereas the pump mechanism is treated within the Born-Markov approximation, the output coupling leads to non-Markovian effects. The solution of the master equation resulting from the time-convolutionless projection operator technique exhibits strong oscillations in the occupation number of the Bose-Einstein condensate. These oscillations are traced back to a quantum interference which is due to the non-Markovian dynamics and which decays slowly in time as a result of the dispersion relation for massive particles.

arXiv:quant-ph/9906119Physical Review AOct 1, 199928 citations

Effects of relative phase and interactions on atom-laser outcoupling from a double-well Bose–Einstein condensate: Markovian and non-Markovian dynamics

Georgios M. Nikolopoulos, Constantinos Lazarou, P. Lambropoulos

We investigate aspects of the dynamics of a continuous atom-laser scheme based on the merging of independently formed atomic condensates. Our theoretical analysis covers the Markovian as well as the non-Markovian operational regimes, and is based on a semiclassical (mean-field) two-mode model. The role of the relative phase between the two condensates and the effect of interatomic interactions on the evolution of the trapped populations and the distribution of outcoupled atoms are discussed.

arXiv:0711.3731Journal of Physics B Atomic Molecular and Optical PhysicsJan 8, 200811 citations

Steady-state quantum statistics of a non-Markovian atom laser. II

Ashton S. Bradley, J. J. Hope, Matthew J. Collett

We present a steady-state analysis of a quantum-mechanical model of an atom laser. A single-mode atomic trap coupled to a continuum of external modes is driven by a saturable pumping mechanism. In the dilute flux regime, where atom-atom interactions are negligible in the output, we find an analytic form for the linewidth and frequency shift of the laser. This result does not make the Born-Markov approximation, but is based on the far less restrictive ``self-consistent Markov approximation.'' The more exact treatment has a different effective damping rate and occupation of the lasing mode, as well as a shifted frequency and linewidth of the output. We examine gravitational damping numerically, finding linewidths and frequency shifts for a range of pumping rates. We treat mean-field damping analytically, finding a memory function for the Thomas-Fermi regime. The occupation and linewidth are found to have a nonlinear scaling behavior which has implications for the stability of atom lasers.

arXiv:cond-mat/0210688Physical Review ADec 22, 20037 citations

Non-Markovian quantum dynamics: A non-perturbative approach combining projection superoperators and Hilbert space averaging

Heinz‐Peter Breuer, Jochen Gemmer B, Mathias Michel A

The time-convolutionless (TCL) projection operator technique allows a systematic analysis of the non-Markovian quantum dynamics of open systems. We introduce a class of projection superoperators which project the states of the total system onto certain correlated system-environment states. It is shown that the application of the TCL technique to this class of correlated superoperators enables the non-perturbative treatment of the dynamics of system-environment models for which the standard approach fails in any finite order of the coupling strength. We demonstrate further that the correlated superoperators correspond to the idea of a best guess of conditional quantum expectations which is determined by a suitable Hilbert space average. The general approach is illustrated by means of the model of a spin which interacts through randomly distributed couplings with a finite reservoir consisting of two energy bands. Extensive numerical simulations of the full Schroedinger equation of the model reveal the power and efficiency of the method.

Oct 24, 20050 citations

The Breakdown of the Born and Markov approximations for atom lasers

G. M. Moy, J. J. Hope, Craig M. Savage

We discuss the use of the Born and Markov approximations in describing the dynamics of an atom laser. In particular, we investigate the applicability of the quantum optical Born-Markov master equation for describing output coupling. We derive conditions based on the atomic reservoir, and atom dispersion relations for when the Born-Markov approximations are valid and discuss parameter regimes where these approximations fail in our atom laser model. Differences between the standard optical laser model and the atom laser are due to a combination of factors, including the parameter regimes in which a typical atom laser would operate, the different reservoir state which is appropriate for atoms, and the different dispersion relations between atoms and photons. We present results based on an exact method in the regimes in which the Born-Markov approximation fails. The exact solutions in some experimentally relavent parameter regimes give non-exponential loss of atoms from a cavity.

Jan 23, 19981 citation

Steady-state quantum statistics of a non-Markovian atom laser

J. J. Hope, G. M. Moy, Matthew J. Collett +1 more

We present a fully quantum-mechanical treatment of a single-mode atomic cavity with a pumping mechanism and an output coupling to a continuum of external modes. This system is a schematic description of an atom laser. In the dilute limit where atom-atom interactions are negligible, we have been able to solve this model without making the Born and Markov approximations. When coupling into free space, it is shown that for reasonable parameters there is a bound state which does not disperse, which means that there is no steady state. This bound state does not exist when gravity is included, and in that case the system reaches a steady state. We develop equations of motion for the two-time correlation in the presence of pumping and gravity in the output modes. We then calculate the energy spectrum of the steady-state output flux from the laser. We present a ``self-consistent Markov approximation'' which allows efficient calculation of this energy spectrum well above threshold.

arXiv:cond-mat/9907023Physical Review AJan 10, 200062 citations