Detecting the breached pair phase in a polarized ultracold Fermi gas

We propose a method for the experimental detection of a new quantum phase, the breached pair state, in a strongly interacting ultracold Fermi gas with population imbalance. We show that through the time-of-flight Raman imaging, the presence of such a phase can be unambiguously determined with a measurement of the momentum-space phase separation of the minority spin component. To guide the experimental efforts, the momentum-space density profiles are calculated under typical experimental conditions.Comment: 4 pages, 3 figures, replaced with the published versio

Trapped Fermions across a Feshbach resonance with population imbalance

We investigate the phase separation of resonantly interacting fermions in a trap with imbalanced spin populations, both at zero and at finite temperatures. We directly minimize the thermodynamical potential under the local density approximation instead of using the gap equation, as the latter may give unstable solutions. On the BEC side of the resonance, one may cross three different phases from the trap center to the edge; while on the BCS side or at resonance, typically only two phases show up. We compare our results with the recent experiment, and the agreement is remarkable.Comment: 4 pages, 3 figures, replaced with the published versio

Thermodynamic properties of a dipolar Fermi gas

Based on the semi-classical theory, we investigate the thermodynamic properties of a dipolar Fermi gas. Through a self-consistent procedure, we numerically obtain the phase space distribution function at finite temperature. We show that the deformations in both momentum and real space becomes smaller and smaller as one increases the temperature. For homogeneous case, we also calculate pressure, entropy, and heat capacity. In particular, at low temperature limit and in weak interaction regime, we obtain an analytic expression for the entropy, which agrees qualitatively with our numerical result. The stability of a trapped gas at finite temperature is also explored

BCS-BEC crossover and quantum phase transition for 6Li and 40K atoms across Feshbach resonance

We systematically study the BCS-BEC crossover and the quantum phase transition in ultracold 6Li and 40K atoms across a wide Feshbach resonance. The background scattering lengths for 6Li and 40K have opposite signs, which lead to very different behaviors for these two types of atoms. For 40K, both the two-body and the many-body calculations show that the system always has two branches of solutions: one corresponds to a deeply bound molecule state; and the other, the one accessed by the current experiments, corresponds to a weakly bound state with population always dominantly in the open channel. For 6Li, there is only a unique solution with the standard crossover from the weakly bound Cooper pairs to the deeply bound molecules as one sweeps the magnetic field through the crossover region. Because of this difference, for the experimentally accessible state of 40K, there is a quantum phase transition at zero temperature from the superfluid to the normal fermi gas at the positive detuning of the magnetic field where the s-wave scattering length passes its zero point. For 6Li, however, the system changes continuously across the zero point of the scattering length. For both types of atoms, we also give detailed comparison between the results from the two-channel and the single-channel model over the whole region of the magnetic field detuning.Comment: 7 pages, 6 figure

Phase diagram of a polarized Fermi gas across a Feshbach resonance in a potential trap

We map out the detailed phase diagram of a trapped ultracold Fermi gas with population imbalance across a wide Feshbach resonance. We show that under the local density approximation, the properties of the atoms in any (anisotropic) harmonic traps are universally characterized by three dimensionless parameters: the normalized temperature, the dimensionless interaction strength, and the population imbalance. We then discuss the possible quantum phases in the trap, and quantitatively characterize their phase boundaries in various typical parameter regions.Comment: 9 pages, 4 figure

Effect of feedback on the control of a two-level dissipative quantum system

We show that it is possible to modify the stationary state by a feedback control in a two-level dissipative quantum system. Based on the geometric control theory, we also analyze the effect of the feedback on the time-optimal control in the dissipative system governed by the Lindblad master equation. These effects are reflected in the function $\Delta_A(\vec{x})$ and $\Delta_B(\vec{x})$ that characterize the optimal trajectories, as well as the switching function $\Phi(t)$ and $\theta(t),$ which characterize the switching point in time for the time-optimal trajectory.Comment: 5 pages, 5 figure

Probing dipolar effects with condensate shape oscillation

We discuss the low energy shape oscillations of a magnetic trapped atomic condensate including the spin dipole interaction. When the nominal isotropic s-wave interaction strength becomes tunable through a Feshbach resonance (e.g. as for $^{85}$Rb atoms), anisotropic dipolar effects are shown to be detectable under current experimental conditions [E. A. Donley {\it et al.}, Nature {\bf 412}, 295 (2001)].Comment: revised version, submitte

The n-body problem in General Relativity up to the second post-Newtonian order from perturbative field theory

Motivated by experimental probes of general relativity, we adopt methods from perturbative (quantum) field theory to compute, up to certain integrals, the effective lagrangian for its n-body problem. Perturbation theory is performed about a background Minkowski spacetime to O[(v/c)^4] beyond Newtonian gravity, where v is the typical speed of these n particles in their center of energy frame. For the specific case of the 2 body problem, the major efforts underway to measure gravitational waves produced by in-spiraling compact astrophysical binaries require their gravitational interactions to be computed beyond the currently known O[(v/c)^7]. We argue that such higher order post-Newtonian calculations must be automated for these field theoretic methods to be applied successfully to achieve this goal. In view of this, we outline an algorithm that would in principle generate the relevant Feynman diagrams to an arbitrary order in v/c and take steps to develop the necessary software. The Feynman diagrams contributing to the n-body effective action at O[(v/c)^6] beyond Newton are derived.Comment: 39 pages. The Mathematica code used in this paper can be found at http://www.stargazing.net/yizen/PN.html Version 2: Slight re-wording of section on removal of accelerations in 2 PN lagrangian; comments added in conclusion; and typographical errors fixed. Article is similar to that published in PR

Signal of Bose condensation in an optical lattice at finite temperature

We discuss the experimental signal for the Bose condensation of cold atoms in an optical lattice at finite temperature. Instead of using the visibility of the interference pattern via the time-of-flight imaging, we show that the momentum space density profile in the first Brillouin zone, in particular its bimodal distribution, provides an unambiguous signal for the Bose condensation. We confirm this point with detailed calculation of the change in the atomic momentum distribution across the condensation phase transition, taking into account both the global trapping potential and the atomic interaction effects.Comment: 4 pages, 2 figures, replaced with the published versio