We consider the problem of a single $\downarrow$ atom in the presence of a Fermi sea of $\uparrow$ atoms, in the vicinity of a Feshbach resonance. We calculate the chemical potential and the effective mass of the $\downarrow$ atom using two simple approaches: a many-body variational wave function and a $T$-matrix approximation. These two methods lead to the same results and are in good agreement with existing quantum Monte Carlo calculations performed at unitarity and, in one dimension, with the known exact solution. Surprisingly, our results suggest that, even at unitarity, the effect of interactions is fairly weak and can be accurately described using single particle-hole excitations. We also consider the case of unequal masses.

There are many cases where the interaction between two qubits is not precisely known, but single-qubit operations are available. In this Letter we show how, regardless of an incomplete knowledge of the strength or form of the interaction between two qubits, it is often possible to construct a controlled-NOT gate which has arbitrarily high fidelity. In particular, we show that oscillations in the strength of the exchange interaction in solid state Si and Ge structures are correctable.

The recombination of two split Bose-Einstein condensates on an atom chip is shown to result in heating which depends on the relative phase of the two condensates. This heating reduces the number of condensate atoms between 10% and 40% and provides a robust way to read out the phase of an atom interferometer without the need for ballistic expansion. The heating may be caused by the dissipation of dark solitons created during the merging of the condensates.

We investigate the time evolution of correlations in the Bose-Hubbard model following a quench from the superfluid to the Mott insulator. For large values of the final interaction strength the system approaches a distinctly nonequilibrium steady state that bears strong memory of the initial conditions. In contrast, when the final interaction strength is comparable to the hopping, the correlations are rather well approximated by those at thermal equilibrium. The existence of two distinct nonequilibrium regimes is surprising given the nonintegrability of the Bose-Hubbard model. We relate this phenomenon to the role of quasiparticle interactions in the Mott insulator.

Hyperfine transitions in the electronic ground state of cold, trapped hydrogenlike highly charged ions have attractive features for use as frequency standards because the majority of systematic frequency shifts are smaller by orders of magnitude compared to many microwave and optical frequency standards. Frequency measurements of these transitions hold promise for significantly improved laboratory tests of local position invariance of the electron and quark masses.

We study an ultracold Bose gas in the presence of 1D disorder for repulsive interatomic interactions varying from zero to the Thomas-Fermi regime. We show that for weak interactions the Bose gas populates a finite number of localized single-particle Lifshits states, while for strong interactions a delocalized disordered Bose-Einstein condensate is formed. We discuss the schematic quantum-state diagram and derive the equations of state for various regimes.

We argue that, for the recent experiments with imbalanced fermion gases, a temperature difference may occur between the normal (N) and the gapped superfluid (SF) phase. Using the mean-field formalism, we study particle scattering off the N-SF interface from the deep BCS to the unitary regime. We show that the thermal conductivity across the interface drops exponentially fast with increasing $h/k_{B}T$, where $h$ is the chemical potential imbalance. This implies a blocking of thermal equilibration between the N and the SF phase. We also provide a possible mechanism for the creation of gap oscillations [Fulde-Ferrell-Larkin-Ovchinnikov (FFLO)-like states] as seen in recent studies on these systems.

Sound waves are excited in an optically trapped degenerate Fermi gas of spin-up and spin-down atoms with magnetically tunable interactions. Measurements are made throughout the crossover region, from a weakly interacting Fermi gas through the resonant Fermi superfluid regime to a Bose condensate of dimer molecules. The measured sound velocities test theories of hydrodynamic wave propagation and predictions of the equation of state. At resonance, the sound velocity exhibits universal scaling with the Fermi velocity, to within 1.8% over a factor of 30 in density.

We present and experimentally demonstrate a novel optical nondestructive controlled-NOT gate without using entangled ancilla. With much fewer measurements compared with quantum process tomography, we get a good estimation of the gate fidelity. The result shows a great improvement compared with previous experiments. Moreover, we also show that quantum parallelism is achieved in our gate and the performance of the gate cannot be reproduced by local operations and classical communications.

We report the first experimental demonstration of continuous variable cloning of phase-conjugate coherent states as proposed by Cerf and Iblisdir [Phys. Rev. Lett. 87, 247903 (2001)]. In contrast to this proposal, the cloning transformation is accomplished using only linear optical components, homodyne detection, and feedforward. As a result of combining phase conjugation with a joint measurement strategy, superior cloning is demonstrated with cloning fidelities reaching 89%.

We discuss stochastic resonance (SR) effects in driven coupled quantum systems. We construct dynamical and information-theoretic measures of the system’s response that exhibit a nonmonotonic behavior as a function of the noise strength. We analyze the relation between lack of monotonicity in the response and the presence of quantum correlations and identify parameter regimes where the breakdown of a linear response can be linked to the presence of entanglement. We also show that a chain of coupled spin systems can exhibit an array-enhanced response, where the sensitivity of a single resonator is enhanced as a result of nearest-neighbor coupling. These results enlarge the domain where SR effects exist and should be observable in arrays of superconducting qubits.

We present exact derivations of the effective capillary wave fluctuation-induced forces resulting from pinning of an interface between two coexisting phases at two points separated by a distance $r$. In two dimensions the Ising ferromagnet calculations based on the transfer matrix approach give an attractive force decaying as $1/r$ for large distances. In three dimensions mapping of the body-centered solid-on-solid model onto the 6-vertex model allows for exact solution using the bosonization analysis of the equivalent $XXZ$ Heisenberg quantum chain. The exact result gives the attractive force which decays asymptotically as $1/(r\log r)$.

We introduce a “microcanonical” measure (complying with the “general canonical principle”) over the second moments of pure bosonic Gaussian states under an energy constraint. We determine the average fidelity for the teleportation of states distributed according to such a measure and compare it to a threshold obtained from a feasible classical strategy. Furthermore, we show that, under the proposed measure, the distribution of the entanglement concentrates around a finite value at the thermodynamical limit and, in general, the typical entanglement of Gaussian states with maximal energy $E$ is not close to the maximum allowed by $E$.

The effect of noise on the nonlinear photoionization of an atom due to a femtosecond pulse is investigated in the framework of the stochastic Schrödinger equation. A modest amount of white noise results in an enhancement of the net ionization yield by several orders of magnitude, giving rise to a form of quantum stochastic resonance. We demonstrate that this effect is preserved if the white noise is replaced by broadband chaotic light.

It is shown that zero point quantum fluctuations completely lift the accidental continuous degeneracy that is found in mean field analysis of quantum spin nematic phases of hyperfine spin-2 cold atoms. The result is two distinct ground states which have higher symmetries: a uniaxial spin nematic and a biaxial spin nematic with dihedral symmetry ${\mathrm{Dih}}_4$. There is a novel first-order quantum phase transition between the two phases as atomic scattering lengths are varied. We find that the ground state of ${}^{87}\mathrm{Rb}$ atoms should be a uniaxial spin nematic. We note that the energy barrier between the phases could be observable in dynamical experiments.

We discuss generalizations of quantum spin Hamiltonians using anyonic degrees of freedom. The simplest model for interacting anyons energetically favors neighboring anyons to fuse into the trivial (“identity”) channel, similar to the quantum Heisenberg model favoring neighboring spins to form spin singlets. Numerical simulations of a chain of Fibonacci anyons show that the model is critical with a dynamical critical exponent $z=1$, and described by a two-dimensional (2D) conformal field theory with central charge $c=\frac{7}{10}$. An exact mapping of the anyonic chain onto the 2D tricritical Ising model is given using the restricted-solid-on-solid representation of the Temperley-Lieb algebra. The gaplessness of the chain is shown to have topological origin.

We formulate and prove a de Finetti representation theorem for finitely exchangeable states of a quantum system consisting of $k$ infinite-dimensional subsystems. The theorem is valid for states that can be written as the partial trace of a pure state $|\Psi ⟩⟨\Psi |$ chosen from a family of subsets $\{{\mathcal{C}}_n\}$ of the full symmetric subspace for $n$ subsystems. We show that such states become arbitrarily close to mixtures of pure power states as $n$ increases. We give a second equivalent characterization of the family $\{{\mathcal{C}}_n\}$.

The parametric dependence of a quantum map under the influence of a rank-1 perturbation is investigated. While the Floquet operator of the map and its spectrum have a common period with respect to the perturbation strength $\lambda$, we show an example in which none of the quasienergies nor the eigenvectors obey the same period: After a periodic increment of $\lambda$, the quasienergy arrives at the nearest higher one, instead of the initial one, exhibiting an anholonomy, which governs another anholonomy of the eigenvectors. An application to quantum state manipulations is outlined.

We show that universal quantum computation can be performed within the ground state of a topologically ordered quantum system, which is a naturally protected quantum memory. In particular, we show how this can be achieved using brane-net condensates in 3-colexes. The universal set of gates is implemented without selective addressing of physical qubits and, being fully topologically protected, it does not rely on quasiparticle excitations or their braiding.

We consider a two-component atomic Fermi gas within a mean-field, single-channel model, where both the mass and population of each component are unequal. We show that the tricritical point at zero temperature evolves smoothly from the BEC to BCS side of the resonance as a function of mass ratio $r$. We find that the interior gap state proposed by Liu and Wilczek is always unstable to phase separation, while the breached pair state with one Fermi surface for the excess fermions exhibits differences in its density of states and pair correlation functions depending on which side of the resonance it lies. Finally, we show that, when $r\gtrsim 3.95$, the finite-temperature phase diagram of trapped gases at unitarity becomes topologically distinct from the equal mass system.