arXiv subjects

J. J. Hope

Publications and source records attributed to J. J. Hope.

52 records · Page 3Linked to original sources

arXiv2003

Control of an atom laser using feedback

A generalised method of using feedback to control Bose-Einstein condensates is introduced. The condensates are modelled by the Gross-Pitaevskii equation, so only semiclassical fluctations can be suppressed, and back-action from the measurement is ignored. We show that for any available control, a feedback scheme can be found to reduce the energy while the appropriate moment is still dynamic. We demonstrate these schemes by considering a condensate trapped in a harmonic potential that can be modulated in strength and position. The formalism of our feedback scheme also allows the inclusion of certain types of non-linear controls. If the non-linear interaction between the atoms can be controlled via a Feshbach resonance, we show that the feedback process can operate with a much higher efficiency.

cond-mat↗

arXiv2003

Limit to non-destructive optical detection of atoms

All optical techniques used to probe the properties of Bose-Einstein condensates have been based on dispersion and absorption that can be described by a two-level atom. Both phenomena lead to spontaneous emission that is destructive. Recently, both were shown to lead to the same limit to the signal to noise ratio for a given destruction. We generalise this result to show that no single-pass optical technique using classical light, based on any number of lasers or coherences between any number of levels, can exceed the limit imposed by the two-level atom. This puts significant restrictions on potential non-destructive measurement schemes.

quant-ph↗

arXiv2003

Non-destructive, dynamic detectors for Bose-Einstein condensates

We propose and analyze a series of non-destructive, dynamic detectors for Bose-Einstein condensates based on photo-detectors operating at the shot noise limit. These detectors are compatible with real time feedback to the condensate. The signal to noise ratio of different detection schemes are compared subject to the constraint of minimal heating due to photon absorption and spontaneous emission. This constraint leads to different optimal operating points for interference-based schemes. We find the somewhat counter-intuitive result that without the presence of a cavity, interferometry causes as much destruction as absorption for optically thin clouds. For optically thick clouds, cavity-free interferometry is superior to absorption, but it still cannot be made arbitrarily non-destructive . We propose a cavity-based measurement of atomic density which can in principle be made arbitrarily non-destructive for a given signal to noise ratio.

cond-mat↗

arXiv2002

Stationary quantum statistics of a non-Markovian atom laser

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 have been able to solve this model without making the Born-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.

cond-mat.soft↗

arXiv2002

Bose-Einstein condensate collapse: a comparison between theory and experiment

We solve the Gross-Pitaevskii equation numerically for the collapse induced by a switch from positive to negative scattering lengths. We compare our results with experiments performed at JILA with Bose-Einstein condensates of Rb-85, in which the scattering length was controlled using a Feshbach resonance. Building on previous theoretical work we identify quantitative differences between the predictions of mean-field theory and the results of the experiments. Besides the previously reported difference between the predicted and observed critical atom number for collapse, we also find that the predicted collapse times systematically exceed those observed experimentally. Quantum field effects, such as fragmentation, that might account for these discrepancies are discussed.

cond-mat↗

arXiv2001

Stability of continuously pumped atom lasers

A multimode model of a continuously pumped atom laser is shown to be unstable below a critical value of the scattering length. Above the critical scattering length, the atom laser reaches a steady state, the stability of which increases with pumping. Below this limit the laser does not reach a steady state. This instability results from the competition between gain and loss for the excited states of the lasing mode. It will determine a fundamental limit for the linewidth of an atom laser beam.

cond-mat↗

arXiv2001

Quantum field effects in coupled atomic and molecular Bose-Einstein condensates

This paper examines the parameter regimes in which coupled atomic and molecular Bose-Einstein condensates do not obey the Gross-Pitaevskii equation. Stochastic field equations for coupled atomic and molecular condensates are derived using the functional positive-P representation. These equations describe the full quantum state of the coupled condensates and include the commonly used Gross-Pitaevskii equation as the noiseless limit. The model includes all interactions between the particles, background gas losses, two-body losses and the numerical simulations are performed in three dimensions. It is found that it is possible to differentiate the quantum and semiclassical behaviour when the particle density is sufficiently low and the coupling is sufficiently strong.

cond-mat↗

arXiv2000

Resonance fluorescence in a band gap material: Direct numerical simulation of non-Markovian evolution

A numerical method of calculating the non-Markovian evolution of a driven atom radiating into a structured continuum is developed. The formal solution for the atomic reduced density matrix is written as a Markovian algorithm by introducing a set of additional, virtual density matrices which follow, to the level of approximation of the algorithm, all the possible trajectories of the photons in the electromagnetic field. The technique is perturbative in the sense that more virtual density matrices are required as the product of the effective memory time and the effective coupling strength become larger. The number of density matrices required is given by $3^{M}$ where $M$ is the number of timesteps per memory time. The technique is applied to the problem of a driven two-level atom radiating close to a photonic band gap and the steady-state correlation function of the atom is calculated.

quant-ph↗

arXiv1999

The steady state quantum statistics of a non-Markovian atom laser

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 steady-state output energy flux from the laser.

cond-mat↗

arXiv1999

The linewidth of a non-Markovian atom laser

We present a fully quantum mechanical treatment of a single mode atom laser including pumping and output coupling. By ignoring atom-atom interactions, we have solved this model without making the Born-Markov approximation. We find substantially less gain narrowing than is predicted under that approximation.

quant-ph↗

arXiv1998

The Born and Markov approximations for atom lasers

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.

quant-ph↗

arXiv1998

The steady state of a pumped and damped atom laser

This paper has been withdrawn, as further work has shown that an atom laser as described by the model herein does not have a steady state, so it doesn't matter much what it would look like.

physics.atom-ph↗

arXiv1997

An Atom Laser Based on Raman Transitions

In this paper we present an atom laser scheme using a Raman transition for the output coupling of atoms. A beam of thermal atoms (bosons) in a metastable atomic state $|1 >$ are pumped into a multimode atomic cavity. This cavity is coupled through spontaneous emission to a single mode of another cavity for the ground atomic state, $|2 >$. Above a certain threshold pumping rate a large number of atoms, $N_2$, builds up in this single quantum state and transitions to the ground state of the cavity become enhanced by a factor $(N_2 + 1)$. Atoms in this state are then coupled to the outside of the cavity with a Raman transition. This changes the internal state of the atom and imparts a momentum kick, allowing the atoms to leave the system.

atom-ph↗

arXiv1996

Stimulation of Beta Decay due to a Bose-Einstein Condensate

Nuclear processes can be stimulated by the presence of a macroscopic number of bosons in one of the final states. We describe the conditions necessary to observe the atom-stimulation of a beta decay process. The stimulation may be observable if it becomes possible to produce a Bose-Einstein condensate with the order of $10^{14}$ atoms in a trap.

atom-ph↗

arXiv1996

Stimulated Enhancement of Cross-Section by a Bose-Einstein Condensate

This paper examines the feasibility of constructing an experiment which detects the atomic stimulation of a photon emission process. A beam of atoms (bosons) in an excited state is passed over an atomic trap which traps the atoms when they are in their internal ground state. When the trap contains a Bose-Einstein condensate, the cross-section for absorption of the atomic beam is increased. We examine a particular model in which this atom-stimulation is observable, and is also characterised by the emission of photons in a narrow cone in the direction of the atomic beam.

atom-ph↗

arXiv1995

Band Gaps for Atoms in Light based Waveguides

The energy spectrum for a system of atoms in a periodic potential can exhibit a gap in the band structure. We describe a system in which a laser is used to produce a mechanical potential for the atoms, and a standing wave light field is used to shift the atomic levels using the Autler-Townes effect, which produces a periodic potential. The band structure for atoms guided by a hollow optical fiber waveguide is calculated in three dimensions with quantised external motion. The size of the band gap is controlled by the light guided by the fiber. This variable band structure may allow the construction of devices which can cool atoms. The major limitation on this device would be the spontaneous emission losses.

atom-ph↗