Comment on ``Phase and Phase Diffusion of a Split Bose-Einstein Condensate''

Recently Javanainen and Wilkens [Phys. Rev. Lett. 78, 4675 (1997)] have analysed an experiment in which an interacting Bose condensate, after being allowed to form in a single potential well, is "cut" by splitting the well adiabatically with a very high potential barrier, and estimate the rate at which, following the cut, the two halves of the condensate lose the "memory" of their relative phase. We argue that, by neglecting the effect of interactions in the initial state before the separation, they have overestimated the rate of phase randomization by a numerical factor which grows with the interaction strength and with the slowness of the separation process.Comment: 2 pages, no figures, to appear in Phys. Rev. Let

On the Supersolid State of Matter

We prove that the necessary condition for a solid to be also a superfluid is to have zero-point vacancies, or interstitial atoms, or both, as an integral part of the ground state. As a consequence, superfluidity is not possible in commensurate solids which break continuous translation symmetry. We discuss recent experiment by Kim and Chan [Nature, {\bf 427}, 225 (2004)] in the context of this theorem, question its bulk supersolid interpretation, and offer an alternative explanation in terms of superfluid helium interfaces.Comment: 4 figures, 4 page

Dissipation-induced d-Wave Pairing of Fermionic Atoms in an Optical Lattice

We show how dissipative dynamics can give rise to pairing for two-component fermions on a lattice. In particular, we construct a "parent" Liouvillian operator so that a BCS-type state of a given symmetry, e.g. a d-wave state, is reached for arbitrary initial states in the absence of conservative forces. The system-bath couplings describe single-particle, number conserving and quasi-local processes. The pairing mechanism crucially relies on Fermi statistics. We show how such Liouvillians can be realized via reservoir engineering with cold atoms representing a driven dissipative dynamics.Comment: 5 pages, 3 figures. Replaced with the published versio

Influence of External Fields and Environment on the Dynamics of Phase Qubit-Resonator System

We analyze the dynamics of a qubit-resonator system coupled with a thermal bath and external electromagnetic fields. Using the evolution equations for the set of Heisenberg operators, that describe the whole system, we derive an expression for the resonator field, accounting for the resonator-drive,-bath, and -qubit interaction. The renormalization of the resonator frequency, caused by the qubit-resonator interaction, is accounted for. Using solutions for the resonator field, we derive the equation describing qubit dynamics. The influence of the qubit evolution during the measurement time on the fidelity of a single-shot measurement is studied. The relation between the fidelity and measurement time is shown explicitly. Also, an expression describing relaxation of the superposition qubit state towards its stationary value is derived. The possibility of controlling this state, by varying the amplitude and frequency of drive, is shown.Comment: 15 page

Feasibility of Experimental Realization of Entangled Bose-Einstein Condensation

We examine the practical feasibility of the experimental realization of the so-called entangled Bose-Einstein condensation (BEC), occurring in an entangled state of two atoms of different species. We demonstrate that if the energy gap remains vanishing, the entangled BEC persists as the ground state of the concerned model in a wide parameter regime. We establish the experimental accessibility of the isotropic point of the effective parameters, in which the entangled BEC is the exact ground state, as well as the consistency with the generalized Gross-Pitaevskii equations. The transition temperature is estimated. Possible experimental implementations are discussed in detail.Comment: 6 pages, published versio

Superfluidity and excitations at unitarity

We present lattice results for spin-1/2 fermions at unitarity, where the effective range of the interaction is zero and the scattering length is infinite. We measure the spatial coherence of difermion pairs for a system of 6, 10, 14, 18, 22, 26 particles with equal numbers of up and down spins in a periodic cube. Using Euclidean time projection, we analyze ground state properties and transient behavior due to low-energy excitations. At asymptotically large values of t we see long-range order consistent with spontaneously broken U(1) fermion-number symmetry and a superfluid ground state. At intermediate times we see exponential decay in the t-dependent signal due to an unknown low-energy excitation. We probe this low-energy excitation further by calculating two-particle correlation functions. We find that the excitation has the properties of a chain of particles extending across the periodic lattice.Comment: 40 pages, 19 figures, revised version includes new data on two-particle density correlation

Thermodynamics of the BCS-BEC crossover

We present a self-consistent theory for the thermodynamics of the BCS-BEC crossover in the normal and superfluid phase which is both conserving and gapless. It is based on the variational many-body formalism developed by Luttinger and Ward and by DeDominicis and Martin. Truncating the exact functional for the entropy to that obtained within a ladder approximation, the resulting self-consistent integral equations for the normal and anomalous Green functions are solved numerically for arbitrary coupling. The critical temperature, the equation of state and the entropy are determined as a function of the dimensionless parameter $1/k_Fa$, which controls the crossover from the BCS-regime of extended pairs to the BEC-regime of tightly bound molecules. The tightly bound pairs turn out to be described by a Popov-type approximation for a dilute, repulsive Bose gas. Even though our approximation does not capture the critical behaviour near the continuous superfluid transition, our results provide a consistent picture for the complete crossover thermodynamics which compare well with recent numerical and field-theoretic approaches at the unitarity point.Comment: published versio

Creation of NOON states by double Fock-state/Bose-Einstein condensates

NOON states (states of the form $|N>_{a}|0>_{b}+|0>_{a}|N>_{b}$ where $a$ and $b$ are single particle states) have been used for predicting violations of hidden-variable theories (Greenberger-Horne-Zeilinger violations) and are valuable in metrology for precision measurements of phase at the Heisenberg limit. We show theoretically how the use of two Fock state/Bose-Einstein condensates as sources in a modified Mach Zender interferometer can lead to the creation of the NOON state in which $a$ and $b$ refer to arms of the interferometer and $N$ is the total number of particles in the two condensates. The modification of the interferometer involves making conditional ``side'' measurements of a few particles near the sources. These measurements put the remaining particles in a superposition of two phase states, which are converted into NOON states by a beam splitter. The result is equivalent to the quantum experiment in which a large molecule passes through two slits. The NOON states are combined in a final beam splitter and show interference. Attempts to detect through which ``slit'' the condensates passed destroys the interference.Comment: 8 pages 5 figure

Spin Injection into a Luttinger Liquid

We study the effect of spin injection into a Luttinger liquid. The spin-injection-detection setup of Johnson and Silsbee is considered; here spins injected into the Luttinger liquid induce, across an interface with a ferromagnetic metal, either a spin-dependent current ($I_s$) or a spin-dependent boundary voltage ($V_s$). We find that the spin-charge separation nature of the Luttinger liquid affects $I_s$ and $V_s$ in a very different fashion. In particular, in the Ohmic regime, $V_s$ depends on the spin transport properties of the Luttinger liquid in essentially the same way as it would in the case of a Fermi liquid. The implications of our results for the spin-injection-detection experiments in the high $T_c$ cuprates are discussed.Comment: 4 pages, REVTEX, 2 figures. Minor changes and corrections to typos. To appear in Phys. Rev. Let

Formation of magnetic impurities and pair-breaking effect in a superfluid Fermi gas

We theoretically investigate a possible idea to introduce magnetic impurities to a superfluid Fermi gas. In the presence of population imbalance ($N_\uparrow>N_\downarrow$, where $N_\sigma$ is the number of Fermi atoms with pseudospin $\sigma=\uparrow,\downarrow$), we show that nonmagnetic potential scatterers embedded in the system are magnetized in the sense that some of excess $\uparrow$-spin atoms are localized around them. They destroy the superfluid order parameter around them, as in the case of magnetic impurity effect discussed in the superconductivity literature. This pair-breaking effect naturally leads to localized excited states below the superfluid excitation gap. To confirm our idea in a simply manner, we treat an attractive Fermi Hubbard model within the mean-field theory at T=0. We self-consistently determine superfluid properties around a nonmagnetic impurity, such as the superfluid order parameter, local population imbalance, as well as single-particle density of states, in the presence of population imbalance. Since the competition between superconductivity and magnetism is one of the most fundamental problems in condensed matter physics, our results would be useful for the study of this important issue in cold Fermi gases.Comment: 27 pages, 14 figure