We measure excitation spectra of an ultracold gas of fermionic ${}^{40}\mathrm{K}$ atoms in the BCS–Bose-Einstein-condensation (BEC) crossover regime. The measurements are performed with a novel spectroscopy that employs a small modulation of the $B$ field close to a Feshbach resonance to give rise to a modulation of the interaction strength. With this method we observe both a collective excitation as well as the dissociation of fermionic atom pairs in the strongly interacting regime. The excitation spectra reveal the binding energy or excitation gap for pairs in the crossover region.

We demonstrate the experimental feasibility of incompressible fractional quantum Hall-like states in ultracold two-dimensional rapidly rotating dipolar Fermi gases. In particular, we argue that the state of the system at filling fraction $\nu =1/3$ is well described by the Laughlin wave function and find a substantial energy gap in the quasiparticle excitation spectrum. Dipolar gases, therefore, appear as natural candidates of systems that allow us to realize these very interesting highly correlated states in future experiments.

The rate of noise-induced escape from a metastable state of a periodically modulated overdamped system is found for an arbitrary modulation amplitude $A$. The instantaneous escape rate displays peaks that vary with the modulation from Gaussian to strongly asymmetric. The prefactor $\nu$ in the period-averaged escape rate depends on $A$ nonmonotonically. Near the bifurcation amplitude $A_c$ it scales as $\nu \propto (A_c-A{)}^{\zeta }$. We identify three scaling regimes, with $\zeta =1/4$, $-1$, and $1/2$.

We report an experimental study on the effect of an external phase noise on the parametric amplification of surface waves. We observe that both the instability growth rate and the wave amplitude above the instability onset are decreased in the presence of noise. We show that all the results can be understood with a deterministic amplitude equation for the wave in which the effect of noise is just to change the forcing term. All the data for the growth rate (respectively the wave amplitude), obtained for different forcing amplitudes and different intensities of the noise, can be collapsed on a single curve using this renormalized forcing in the presence of noise.

In protocols of distributed quantum information processing, a network of bilateral entanglement is a key resource for efficient communication and computation. We propose a model, efficient both in finite and infinite Hilbert spaces, that performs entanglement distribution among the elements of a network without local control. In the establishment of entangled channels, our setup requires only the proper preparation of a single elected element. We suggest a setup of electromechanical systems to implement our proposal.

I propose a new method to study computationally difficult problems. I consider a new system, larger than the one I want to simulate. The original system is recovered by imposing constraints on the large system. I simulate the large system with the hard constraints replaced by soft constraints. I illustrate the method in the case of a ferromagnetic Ising model and in the case of a three-dimensional spin-glass model. I show that in both models the phases of the soft problem have the same properties as the phases of the original model and that the softened model belongs to the same universality class as the original one. I show that correlation times are much shorter in the larger soft constrained system and that it is computationally advantageous to study it instead of the original system. This method is quite general and can be applied to many other systems.

We calculate the oscillation frequencies of trapped Fermi condensate with particular emphasis on the equation of state of the interacting Fermi system. We confirm Stringari’s finding that the frequencies are independent of the interaction in the unitary limit, and we extend the theory away from that limit, where the interaction does affect the frequencies of the compressional modes only.

It is proposed that the spatially modulated superfluid phase, or the Fulde-Ferrell-Larkin-Ovchinnikov state could be observed in resonant fermion atomic condensates which are realized recently. We examine optimal experimental setups to achieve it by solving the Bogoliubov–de Gennes equation for both idealized one-dimensional and realistic three-dimensional cases. The spontaneous modulation of this superfluid is shown to be directly imaged as the density profiles either by optical absorption or by Stern-Gerlach experiments.

In measurements of small signals using spin precession the precession angle usually grows linearly in time. We show that a dynamic instability caused by spin interactions can lead to an exponentially growing spin-precession angle, amplifying small signals and raising them above the noise level of a detection system. We demonstrate amplification by a factor of greater than 8 of a spin-precession signal due to a small magnetic field gradient in a spherical cell filled with hyperpolarized liquid ${}^{129}\mathrm{X}\mathrm{e}$. This technique can improve the sensitivity in many measurements that are limited by the noise of the detection system, rather than the fundamental spin-projection noise.

We present entanglement witness operators for detecting genuine multipartite entanglement. These witnesses are robust against noise and require only two local measurement settings when used in an experiment, independent of the number of qubits. This allows detection of entanglement for an increasing number of parties without a corresponding increase in effort. The witnesses presented detect states close to Greenberger-Horne-Zeilinger, cluster, and graph states. Connections to Bell inequalities are also discussed.

We present a general control-theoretic framework for constructing and analyzing random decoupling schemes, applicable to quantum dynamical control of arbitrary finite-dimensional composite systems. The basic idea is to design the control propagator according to a random rather than deterministic path on a group. We characterize the performance of random decoupling protocols, and identify control scenarios where they can significantly weaken time scale requirements as compared to cyclic counterparts. Implications for reliable quantum computation are discussed.

We revisit the question of the relation between entanglement, entropy, and area for harmonic lattice Hamiltonians corresponding to discrete versions of real free Klein-Gordon fields. For the ground state of the $d$-dimensional cubic harmonic lattice we establish a strict relationship between the surface area of a distinguished hypercube and the degree of entanglement between the hypercube and the rest of the lattice analytically, without resorting to numerical means. We outline extensions of these results to longer ranged interactions, finite temperatures, and for classical correlations in classical harmonic lattice systems. These findings further suggest that the tools of quantum information science may help in establishing results in quantum field theory that were previously less accessible.

We study one-dimensional disordered bosons with strong repulsive interactions. A Bose-Fermi mapping expresses this problem in terms of noninteracting Anderson-localized fermions, whereby known results for the distribution function of the local density of states, the spectral statistics, and density-density correlations can be transferred to this new domain of applicability. We show that disorder destroys bosonic quasi-long-range order by calculating the momentum distribution, and comment on the experimental observability of these predictions in ultracold atomic gases.

We theoretically examine a system of Fermi degenerate atoms coupled to bosonic molecules by a Feshbach resonance, focusing on the superfluid transition to a molecular Bose-Einstein condensate dressed by Cooper pairs of atoms. This problem raises interest because it is unclear at present whether bimodal density distributions observed recently in ${}^{40}\mathrm{K}$ and ${}^6\mathrm{L}\mathrm{i}$ are due to a condensate of bosonic molecules or fermionic atom pairs. As opposed to ${}^{40}\mathrm{K}$, we find that any measurable fraction of above-threshold bosonic molecules is necessarily absent for the ${}^6\mathrm{L}\mathrm{i}$ system in question, which strongly implicates Cooper pairs as the culprit behind its bimodal distributions.

We study density profiles in trapped fermionic gases, near Feshbach resonances, at all $T\le T_c$ and in the near Bose-Einstein condensation and unitary regimes. For the latter, we characterize and quantify the generally neglected contribution from noncondensed Cooper pairs. As a consequence of these pairs, our profiles are rather well fit to a Thomas-Fermi (TF) functional form, and equally well fit to experimental data. Our work lends support to the notion that TF fits can be used in an experimental context to obtain information about the temperature.

An exact “branch by branch” calculation of the diffusional flux is proposed for partially absorbed random walks on arbitrary tree structures. In the particular case of symmetric trees, an explicit analytical expression is found which is valid whatever the size of the tree. Its application to the respiratory phenomena in pulmonary acini gives an analytical description of the crossover regime governing the human lung efficiency.

The effect of a uniformly moving medium on the decay rate of an excited atom is calculated. When the local field effects are neglected, the free space decay rate is modified by a factor which is a complicated function of refractive index, permeability, and velocity of the medium. It is shown that the decay rate vanishes if the velocity of the medium exceeds the phase velocity of light in the stationary medium.

A sharp resonance line that appears in three-photon transitions between the ${}^{1}S_0$ and ${}^{3}P_0$ states of alkaline earth and Yb atoms is proposed as an optical frequency standard. This proposal permits the use of the even isotopes, in which the clock transition is narrower than in proposed clocks using the odd isotopes and the energy interval is not affected by external magnetic fields or the polarization of trapping light. With this method, the width and the rate of the clock transition can, in principle, be continuously adjusted from the MHz level to sub-mHz without loss of signal amplitude by varying the intensities of the three optical beams. Doppler and recoil effects can be eliminated by proper alignment of the three optical beams or by point confinement in a lattice trap. Light-shift effects on the clock accuracy can be limited to below a part in ${10}^{18}$.

We present a family of exact solutions of the one-dimensional nonlinear Schrödinger equation which describes the dynamics of a bright soliton in Bose-Einstein condensates with the time-dependent interatomic interaction in an expulsive parabolic potential. Our results show that, under a safe range of parameters, the bright soliton can be compressed into very high local matter densities by increasing the absolute value of the atomic scattering length, which can provide an experimental tool for investigating the range of validity of the one-dimensional Gross-Pitaevskii equation. We also find that the number of atoms in the bright soliton keeps dynamic stability: a time-periodic atomic exchange is formed between the bright soliton and the background.

We investigate unconventional superfluidity in a gas of Fermi atoms with an anisotropic $p$-wave Feshbach resonance. Including the $p$-wave Feshbach resonance as well as the associated three kinds of quasimolecules with finite orbital angular momenta $L_z=\pm 1,0$, we calculate the transition temperature of the superfluid phase. As one passes through the $p$-wave Feshbach resonance, we find the usual BCS-BEC crossover phenomenon. The $p$-wave BCS state continuously changes into the BEC of bound molecules with $L=1$. Our calculation includes the effect of fluctuations associated with Cooper pairs and molecules which are not Bose condensed.