We propose a coherent framework allowing one to treat many-body effects in dense ultracold Fermi gases in the presence of a Feshbach resonance. We show that the simple effect of Pauli exclusion induces a strong modification of the basic scattering properties. In particular, this washes out the Feshbach resonance and provides a natural explanation for recent experimental findings.

The second law of thermodynamics in nonextensive statistical mechanics is discussed in the quantum regime. Making use of the convexity property of the generalized relative entropy associated with the Tsallis entropy indexed by $q$, Clausius’ inequality is shown to hold in the range $q\in (0,2]$. This restriction on the range of the entropic index, $q$, is purely quantum mechanical and there exists no upper bound of $q$ for validity of the second law in classical theory.

The classical and quantum dynamics in a high frequency field are found to be described by an effective time independent Hamiltonian. It is calculated in a systematic expansion in the inverse of the frequency ($\omega$) to order ${\omega }^{-4}$. The work is an extension of the classical result for the Kapitza pendulum, which was calculated in the past to order ${\omega }^{-2}$. The analysis makes use of an implementation of the method of separation of time scales and of a quantum gauge transformation in the framework of Floquet theory. The effective time independent Hamiltonian enables one to explore the dynamics in the presence of rapidly oscillating fields, in the framework of theories that were developed for systems with time independent Hamiltonians. The results are relevant, in particular, for exploring the dynamics of cold atoms.

Two trapped ions that are kilometers apart can be entangled by the joint detection of two photons, each coming from one of the ions, in a basis of entangled states. Such a detection is possible with linear optical elements. The use of two-photon interference allows entanglement distribution free of interferometric sensitivity to the path length of the photons. The present method of creating entangled ions also opens up the possibility of a loophole-free test of Bell’s inequalities.

We present a coherent filtering scheme which dramatically reduces the site occupation number defects for atoms in an optical lattice by transferring a chosen number of atoms to a different internal state via adiabatic passage. With the addition of superlattices it is possible to engineer states with a specific number of atoms per site (atomic crystals), which are required for quantum computation and the realization of models from condensed matter physics, including doping and spatial patterns. The same techniques can be used to measure two-body spatial correlation functions.

We analyze the macroscopic dynamics of a Bose gas in a harmonic trap with a superimposed two-dimensional optical lattice, assuming a weak coupling between different lattice sites. We consider the situation in which the local chemical potential at each lattice site can be considered as that provided by the Lieb-Liniger solution. Because of the weak coupling between sites and the form of the chemical potential, the three-dimensional ground-state density profile and the excitation spectrum acquire remarkable properties different from both 1D and 3D gases. We call this system a quasi-Tonks gas. We discuss the range of applicability of this regime, as well as realistic experimental situations where it can be observed.

We calculate the in-plane modes of the vortex lattice in a rotating Bose condensate, from the slowly rotating to mean-field quantum Hall limits. The Tkachenko mode frequency, linear in wave vector $k$ for lattice rotational velocities $\Omega$ much smaller than the lowest sound wave frequency in a finite system, becomes quadratic in $k$ in the opposite limit. The system also supports an inertial mode of frequency $\ge 2\Omega$. The calculated frequencies are in excellent agreement with recent observations of Tkachenko modes by I. Coddington, P. Engels, V. Schweikhard, and E. A. Cornell, Phys. Rev. Lett. 91, 100402 (2003).

Heat fluctuations are studied in a dissipative system with both deterministic and stochastic components for a simple model: a Brownian particle dragged through water by a moving potential. An extension of the stationary state fluctuation theorem is derived. For infinite time, this reduces to the conventional fluctuation theorem only for small fluctuations; for large fluctuations, it gives a much larger ratio of the probabilities of the particle to absorb rather than supply heat. This persists for finite times and should be observable in experiments similar to a recent one carried out by Wang et al.

We directly image Tkachenko waves in a vortex lattice in a dilute-gas Bose-Einstein condensate. The low (sub-Hz) resonant frequencies are a consequence of the small but nonvanishing elastic shear modulus of the vortex-filled superfluid. The frequencies are measured for rotation rates as high as 98% of the centrifugal limit for the harmonically confined gas. Agreement with a hydrodynamic theory worsens with increasing rotation rate, perhaps due to the increasing fraction of the volume displaced by the vortex cores. We also observe two low-lying $m=0$ longitudinal modes at about 20 times higher frequency.

Examples of geometric phases abound in many areas of physics. They offer both fundamental insights into many physical phenomena and lead to interesting practical implementations. One of them, as indicated recently, might be an inherently fault-tolerant quantum computation. This, however, requires one to deal with geometric phases in the presence of noise and interactions between different physical subsystems. Despite the wealth of literature on the subject of geometric phases very little is known about this very important case. Here we report the first experimental study of geometric phases for mixed quantum states. We show how different they are from the well-understood, noiseless, pure-state case.

We discuss the possibility of phase conjugation of an atomic Fermi field via nonlinear wave mixing in an ultracold gas. It is shown that for a beam of fermions incident on an atomic phase-conjugate mirror, a time-reversed backward propagating fermionic beam is generated similar to the case in nonlinear optics. By adopting an operational definition of the phase, we show that it is possible to infer the presence of the phase-conjugate field by the loss of the interference pattern in an atomic interferometer.

The effect of fluctuations in the classical control parameters on the Berry phase of a spin $1/2$ interacting with an adiabatically cyclically varying magnetic field is analyzed. It is explicitly shown that in the adiabatic limit dephasing is due to fluctuations of the dynamical phase.

The geometric phase for a pure quantal state undergoing an arbitrary evolution is a “memory” of the geometry of the path in the projective Hilbert space of the system. We find that Uhlmann’s geometric phase for a mixed quantal state undergoing unitary evolution depends not only on the geometry of the path of the system alone but also on a constrained bilocal unitary evolution of the purified entangled state. We analyze this in general, illustrate it for the qubit case, and propose an experiment to test this effect. We also show that the mixed state geometric phase proposed recently in the context of interferometry requires unilocal transformations and is therefore essentially a property of the system alone.

Using tomographic reconstruction we determine the complete internuclear quantum state, represented by the Wigner function, of a dissociating ${\mathrm{I}}_2$ molecule based on femtosecond time resolved position and momentum distributions of the atomic fragments. The experimental data are recorded by timed ionization of the photofragments with an intense 20 fs laser pulse. Our reconstruction method, which relies on Jaynes’s maximum entropy principle, will also be applicable to time resolved position or momentum data obtained with other experimental techniques.

This paper addresses the drag force and formation of vortices in the boundary layer of a Bose-Einstein condensate stirred by a laser beam following the experiments of C. Raman et al., Phys. Rev. Lett. 83, 2502 (1999). We make our analysis in the frame moving at constant speed where the beam is fixed. We find that there is always a drag around the laser beam. We also analyze the mechanism of vortex nucleation. At low velocity, there are no vortices and the drag has its origin in a wakelike phenomenon: This is a particularity of trapped systems since the density gets small in an extended region. The shedding of vortices starts only at a threshold velocity and is responsible for a large increase in drag. This critical velocity for vortex nucleation is lower than the critical velocity computed for the corresponding 2D problem at the center of the cloud.

We demonstrate quantum interference for tetraphenylporphyrin, the first biomolecule exhibiting wave nature, and for the fluorofullerene ${\mathrm{C}}_{60}{\mathrm{F}}_{48}$ using a near-field Talbot-Lau interferometer. For the porphyrins, which are distinguished by their low symmetry and their abundant occurrence in organic systems, we find the theoretically expected maximal interference contrast and its expected dependence on the de Broglie wavelength. For ${\mathrm{C}}_{60}{\mathrm{F}}_{48}$, the observed fringe visibility is below the expected value, but the high contrast still provides good evidence for the quantum character of the observed fringe pattern. The fluorofullerenes therefore set the new mark in complexity and mass (1632 amu) for de Broglie wave experiments, exceeding the previous mass record by a factor of 2.

We have observed a three-dimensional gyroscopic effect associated with a vortex in a dilute Bose-Einstein condensed gas. A condensate with a vortex possesses a single quantum of circulation, and this causes the plane of oscillation of the scissors mode to precess around the vortex line. We have measured the precession rate of the scissors oscillation. From this we deduced the angular momentum associated with the vortex line and found a value close to $\hslash$ per particle, as predicted for a superfluid.

We derive exact closed-form expressions for the first few terms of the short-distance Taylor expansion of the one-body correlation function of the Lieb-Liniger gas. As an intermediate result, we obtain the high-$p$ asymptotics of the momentum distribution of both free and harmonically trapped atoms and show that it obeys a universal $1/p^4$ law for all values of the interaction strength. We discuss the ways to observe the predicted momentum distributions experimentally, regarding them as a sensitive identifier for the Tonks-Girardeau regime of strong correlations.

We describe a general technique that allows one to induce and control strong interaction between spin states of neighboring atoms in an optical lattice. We show that the properties of spin exchange interactions, such as magnitude, sign, and anisotropy, can be designed by adjusting the optical potentials. We illustrate how this technique can be used to efficiently “engineer” quantum spin systems with desired properties, for specific examples ranging from scalable quantum computation to probing a model with complex topological order that supports exotic anyonic excitations.

We study the formation of bright solitons in a Bose-Einstein condensate of ${}^7\mathrm{L}\mathrm{i}$ atoms induced by a sudden change in the sign of the scattering length from positive to negative, as reported in a recent experiment [Nature (London) 417, 150 (2002)]. The numerical simulations are performed by using the Gross-Pitaevskii equation with a dissipative three-body term. We show that a number of bright solitons is produced and this can be interpreted in terms of the modulational instability of the time-dependent macroscopic wave function of the Bose condensate. In particular, we derive a simple formula for the number of solitons that is in good agreement with the numerical results. We find that during the motion of the soliton train in an axial harmonic potential the number of solitonic peaks changes in time and the density of individual peaks shows an intermittent behavior.