Quantum turbulence and correlations in Bose-Einstein condensate collisions

We investigate numerically simulated collisions between experimentally realistic Bose-Einstein condensate wavepackets, within a regime where highly populated scattering haloes are formed. The theoretical basis for this work is the truncated Wigner method, for which we present a detailed derivation, paying particular attention to its validity regime for colliding condensates. This paper is an extension of our previous Letter [A. A. Norrie, R. J. Ballagh, and C. W. Gardiner, Phys. Rev. Lett. 94, 040401 (2005)] and we investigate both single-trajectory solutions, which reveal the presence of quantum turbulence in the scattering halo, and ensembles of trajectories, which we use to calculate quantum-mechanical correlation functions of the field

Quantum turbulence in condensate collisions: an application of the classical field method

We apply the classical field method to simulate the production of correlated atoms during the collision of two Bose-Einstein condensates. Our non-perturbative method includes the effect of quantum noise, and provides for the first time a theoretical description of collisions of high density condensates with very large out-scattered fractions. Quantum correlation functions for the scattered atoms are calculated from a single simulation, and show that the correlation between pairs of atoms of opposite momentum is rather small. We also predict the existence of quantum turbulence in the field of the scattered atoms--a property which should be straightforwardly measurable.Comment: 5 pages, 3 figures: Rewritten text, replaced figure

Theory of the cold collision frequency shift in 1S--2S spectroscopy of Bose-Einstein-condensed and non-condensed hydrogen

We show that a correct formulation of the cold collision frequency shift for two photon spectroscopy of Bose-condensed and cold non-Bose-condensed hydrogen is consistent with experimental data. Our treatment includes transport and inhomogeneity into the theory of a non-condensed gas, which causes substantial changes in the cold collision frequency shift for the ordinary thermal gas, as a result of the very high frequency (3.9kHz) of transverse trap mode. For the condensed gas, we find substantial corrections arise from the inclusion of quasiparticles, whose number is very large because of the very low frequency (10.2Hz) of the longitudinal trap mode. These two effects together account for the apparent absence of a "factor of two" between the two possibilities. Our treatment considers only the Doppler-free measurements, but could be extended to Doppler-sensitive measurements. For Bose-condensed hydrogen, we predict a characteristic "foot" extending into higher detunings than can arise from the condensate alone, as a result of a correct treatment of the statistics of thermal quasiparticles.Comment: 16 page J Phys B format plus 6 postscript figure

Three-body recombination of ultracold Bose gases using the truncated Wigner method

We apply the truncated Wigner method to the process of three-body recombination in ultracold Bose gases. We find that within the validity regime of the Wigner truncation for two-body scattering, three-body recombination can be treated using a set of coupled stochastic differential equations that include diffusion terms, and can be simulated using known numerical methods. As an example we investigate the behaviour of a simple homogeneous Bose gas.Comment: Replaced paper same as original; correction to author list on cond-mat mad

Correcting low-frequency noise with continuous measurement

Low-frequency noise presents a serious source of decoherence in solid-state qubits. When combined with a continuous weak measurement of the eigenstates, the low-frequency noise induces a second-order relaxation between the qubit states. Here we show that the relaxation provides a unique approach to calibrate the low-frequency noise in the time-domain. By encoding one qubit with two physical qubits that are alternatively calibrated, quantum logic gates with high fidelity can be performed.Comment: 10 pages, 3 figures, submitte

Bogoliubov dynamics of condensate collisions using the positive-P representation

We formulate the time-dependent Bogoliubov dynamics of colliding Bose-Einstein condensates in terms of a positive-P representation of the Bogoliubov field. We obtain stochastic evolution equations for the field which converge to the full Bogoliubov description as the number of realisations grows. The numerical effort grows linearly with the size of the computational lattice. We benchmark the efficiency and accuracy of our description against Wigner distribution and exact positive-P methods. We consider its regime of applicability, and show that it is the most efficient method in the common situation - when the total particle number in the system is insufficient for a truncated Wigner treatment.Comment: 9 pages. 5 figure

Theory of the Ramsey spectroscopy and anomalous segregation in ultra-cold rubidium

The recent anomalous segregation experiment of Lewandowski et al. (PRL, 88, 070403, 2002) shows dramatic, rapid internal state segregation for two hyperfine levels of rubidium. We simulate an effective one dimensional model of the system for experimental parameters and find reasonable agreement with the data. The Ramsey frequency is found to be insensitive to the decoherence of the superposition, and is only equivalent to the interaction energy shift for a pure superposition. A Quantum Boltzmann equation describing collisions is derived using Quantum Kinetic Theory, taking into account the different scattering lengths of the internal states. As spin-wave experiments are likely to be attempted at lower temperatures we examine the effect of degeneracy on decoherence by considering the recent experiment of Lewandowski et al. where degeneracy is around 10%. We also find that the segregation effect is only possible when transport terms are included in the equations of motion, and that the interactions only directly alter the momentum distributions of the states. The segregation or spin wave effect is thus entirely due to coherent atomic motion as foreseen in the experimental reportComment: 26 pages, 4 figures, to be published in J. Phys.

Tripartite entanglement and threshold properties of coupled intracavity downconversion and sum-frequency generation

The process of cascaded downconversion and sum-frequency generation inside an optical cavity has been predicted to be a potential source of three-mode continuous-variable entanglement. When the cavity is pumped by two fields, the threshold properties have been analysed, showing that these are more complicated than in well-known processes such as optical parametric oscillation. When there is only a single pumping field, the entanglement properties have been calculated using a linearised fluctuation analysis, but without any consideration of the threshold properties or critical operating points of the system. In this work we extend this analysis to demonstrate that the singly pumped system demonstrates a rich range of threshold behaviour when quantisation of the pump field is taken into account and that asymmetric polychromatic entanglement is available over a wide range of operational parameters.Comment: 24 pages, 15 figure