How do sound waves in a Bose-Einstein condensate move so fast?

Low-momentum excitations of a dilute Bose-Einstein condensate behave as phonons and move at a finite velocity v_s. Yet the atoms making up the phonon excitation each move very slowly; v_a = p/m --> 0. A simple "cartoon picture" is suggested to understand this phenomenon intuitively. It implies a relation v_s/v_a = N_ex, where N_ex is the number of excited atoms making up the phonon. This relation does indeed follow from the standard Bogoliubov theory.Comment: 6 pages, 2 figures (.eps), LaTeX2e. More introductory discussion adde

Storing and processing optical information with ultra-slow light in Bose-Einstein condensates

We theoretically explore coherent information transfer between ultra-slow light pulses and Bose-Einstein condensates (BECs) and find that storing light pulses in BECs, by switching off the coupling field, allows the coherent condensate dynamics to process optical information. We develop a formalism, applicable in both the weak and strong probe regimes, to analyze such experiments and establish several new results. Investigating examples relevant to Rb-87 experimental parameters we see a variety of novel two-component BEC dynamics occur during the storage, including interference fringes, gentle breathing excitations, and two-component solitons. We find the dynamics when the levels |F=1, M_F=-1> and |F=2, M_F=+1> are well suited to designing controlled processing of the information. By switching the coupling field back on, the processed information is rewritten onto probe pulses which then propagate out as slow light pulses. We calculate the fidelity of information transfer between the atomic and light fields upon the switch-on and subsequent output. The fidelity is affected both by absorption of small length scale features and absorption of regions of the pulse stored near the condensate edge. In the strong probe case, we find that when the oscillator strengths for the two transitions are equal the fidelity is not strongly sensitive to the probe strength, while when they are unequal the fidelity is worse for stronger probes. Applications to distant communication between BECs, squeezed light generation and quantum information are anticipated.Comment: 19 pages, 12 figures, submitted to Phys. Rev.

Bragg spectroscopy with an accelerating Bose-Einstein condensate

We present the results of Bragg spectroscopy performed on an accelerating Bose-Einstein condensate. The Bose condensate undergoes circular micro-motion in a magnetic TOP trap and the effect of this motion on the Bragg spectrum is analyzed. A simple frequency modulation model is used to interpret the observed complex structure, and broadening effects are considered using numerical solutions to the Gross-Pitaevskii equation.Comment: 5 pages, 3 figures, to appear in PRA. Minor changes to text and fig

Momentum-Transfer to and Elementary-Excitations of a Bose-Einstein Condensate by a Time-Dependent Optical Potential

We present results of calculations on Bose-Einstein condensed $^{87}$Rb atoms subjected to a moving standing-wave light-potential of the form $V_L(z,t) = V_0(t) \cos(q z-\omega t)$. We calculate the mean-field dynamics (the order paramter) of the condensate and determine the resulting condensate momentum in the $z$ direction, $P_z(q,\omega,V_0,t_p)$, where $V_0$ is the peak optical potential strength and $t_p$ is the pulse duration. Although the local density approximation for the Bogoliubov excitation spectral distribution is a good approximation for very low optical intensities, long pulse duration and sufficiently large values of the wavevector $q$ of the light-potential, for small $q$, short duration pulses, or for not-so-low intensities, the local density perturbative description of the excitation spectrum breaks down badly, as shown by our results.Comment: 8 pages, 7 figure

Four-Wave mixing in degenerate Fermi gases: Beyond the undepleted pump approximation

We analyze the full nonlinear dynamics of the four-wave mixing between an incident beam of fermions and a fermionic density grating. We find that when the number of atoms in the beam is comparable to the number of atoms forming the grating, the dephasing of that grating, which normally leads to a decay of its amplitude, is suppressed. Instead, the density grating and the beam density exhibit large nonlinear coupled amplitude oscillations. In this case four-wave mixing can persist for much longer times compared to the case of negligible back-action. We also evaluate the efficiency of the four-wave mixing and show that it can be enhanced by producing an initial density grating with an amplitude that is less than the maximum value. These results indicate that efficient four-wave mixing in fermionic alkali gases should be experimentally observable.Comment: 9 pages, 8 figure

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.Comment: 6 pages, 7 figure

Metastable neon collisions: anisotropy and scattering length

In this paper we investigate the effective scattering length $a$ of spin-polarized Ne*. Due to its anisotropic electrostatic interaction, its scattering length is determined by five interaction potentials instead of one, even in the spin-polarized case, a unique property among the Bose condensed species and candidates. Because the interaction potentials of Ne* are not known accurately enough to predict the value of the scattering length, we investigate the behavior of $a$ as a function of the five phase integrals corresponding to the five interaction potentials. We find that the scattering length has five resonances instead of only one and cannot be described by a simple gas-kinetic approach or the DIS approximation. However, the probability for finding a positive or large value of the scattering length is not enhanced compared to the single potential case. The complex behavior of $a$ is studied by comparing a quantum mechanical five-channel numerical calculation to simpler two-channel models. We find that the induced dipole-dipole interaction is responsible for coupling between the different |\Omega> states, resulting in an inhomogeneous shift of the resonance positions and widths in the quantum mechanical calculation as compared to the DIS approach. The dependence of the resonance positions and widths on the input potentials turns out to be rather straightforward. The existence of two bosonic isotopes of Ne* enables us to choose the isotope with the most favorable scattering length for efficient evaporative cooling towards the Bose-Einstein Condensation transition, greatly enhancing the feasibility to reach this transition.Comment: 13pages, 8 eps figures, analytical model in section V has been remove

Dynamics of Fermionic Four-Wave Mixing

We study the dynamics of a beam of fermions diffracted off a density grating formed by fermionic atoms in the limit of a large grating. An exact description of the system in terms of particle-hole operators is developed. We use a combination of analytical and numerical methods to quantitatively explore the Raman-Nath and the Bragg regimes of diffraction. We discuss the limits in diffraction efficiency resulting from the dephasing of the grating due the distribution of energy states occupied by the fermions. We propose several methods to overcome these limits, including the novel technique of ``atom echoes''.Comment: 8 pages, 7 figure