We determine some exact static and time-dependent properties of the fermionic Tonks-Girardeau (FTG) gas, a spin-aligned one-dimensional Fermi gas with infinitely strongly attractive zero-range odd-wave interactions. We show that its two-particle reduced density matrix exhibits superconductive off-diagonal long-range order, and on a ring an FTG gas with an even number of atoms has a highly degenerate ground state with quantization of Coriolis rotational flux and high sensitivity to rotation and to external fields and accelerations. For a gas initially under harmonic confinement, we show that during an expansion the momentum distribution undergoes a “dynamical bosonization,” approaching that of an ideal Bose gas without violating the Pauli exclusion principle.

We investigate Gaussian quantum states in view of their exceptional role within the space of all continuous variables states. A general method for deriving extremality results is provided and applied to entanglement measures, secret key distillation and the classical capacity of bosonic quantum channels. We prove that for every given covariance matrix the distillable secret key rate and the entanglement, if measured appropriately, are minimized by Gaussian states. This result leads to a clearer picture of the validity of frequently made Gaussian approximations. Moreover, it implies that Gaussian encodings are optimal for the transmission of classical information through bosonic channels, if the capacity is additive.

Fermion antibunching was observed on a beam of free noninteracting neutrons. A monochromatic beam of thermal neutrons was first split by a graphite single crystal, then fed to two detectors, displaying a reduced coincidence rate. The result is a fermionic complement to the Hanbury Brown and Twiss effect for photons.

We find the exact Casimir force between a plate and a cylinder, a geometry intermediate between parallel plates, where the force is known exactly, and the plate sphere, where it is known at large separations. The force has an unexpectedly weak decay $\sim L/[H^3\ln (H/R)]$ at large plate-cylinder separations $H$ ($L$ and $R$ are the cylinder length and radius), due to transverse magnetic modes. Path integral quantization with a partial wave expansion additionally gives a qualitative difference for the density of states of electric and magnetic modes, and corrections at finite temperatures.

A strongly interacting Fermi gas, such as that of cold atoms operative near a Feshbach resonance, is difficult to study by perturbative many-body theory to go beyond mean-field approximation. Here I develop an effective field theory for the resonant superfluid based on broken symmetry. The theory retains both fermionic quasiparticles and superfluid phonons, the interaction between them being derived nonperturbatively. The theory converges and can be improved order by order, in a manner governed by a low energy expansion rather than by a coupling constant. I apply the effective theory to calculate the specific heat and discuss the theory with a recent heat capacity experiment.

We investigate how entanglement can be transferred between qubits and continuous-variable (CV) systems. We find that one ebit borne in maximally entangled qubits can be fully transferred to two CV systems which are initially prepared in a pure separable Gaussian field with high excitation. We show that it is possible to retrieve the entanglement back to qubits from the entangled CV systems. The deposition of multiple ebits from qubits to the initially separable CV systems is also pointed out. We show that the entanglement transfer and retrieval are done at a quasisteady state.

We study the propagation of a noninteracting atom laser distorted by the strong lensing effect of the Bose-Einstein condensate (BEC) from which it is outcoupled. We observe a transverse structure containing caustics that vary with the density within the residing BEC. Using the WKB approximation, Fresnel-Kirchhoff integral formalism, and $ABCD$ matrices, we are able to describe analytically the atom-laser propagation. This allows us to characterize the quality of the nonideal atom-laser beam by a generalized $M^2$ factor defined in analogy to photon lasers. Finally we measure this quality factor for different lensing effects.

Propagation of the Wigner function is studied on two levels of semiclassical propagation: one based on the Van Vleck propagator, the other on phase-space path integration. Leading quantum corrections to the classical Liouville propagator take the form of a time-dependent quantum spot. Its oscillatory structure depends on whether the underlying classical flow is elliptic or hyperbolic. It can be interpreted as the result of interference of a pair of classical trajectories, indicating how quantum coherences are to be propagated semiclassically in phase space. The phase-space path-integral approach allows for a finer resolution of the quantum spot in terms of Airy functions.

In a topological quantum computer, universal quantum computation is performed by dragging quasiparticle excitations of certain two dimensional systems around each other to form braids of their world lines in $2+1$ dimensional space-time. In this Letter we show that any such quantum computation that can be done by braiding $n$ identical quasiparticles can also be done by moving a single quasiparticle around $n-1$ other identical quasiparticles whose positions remain fixed.

We describe a novel protocol for a quantum repeater that enables long-distance quantum communication through realistic, lossy photonic channels. Contrary to previous proposals, our protocol incorporates active purification of arbitrary errors at each step of the protocol using only two qubits at each repeater station. Because of these minimal physical requirements, the present protocol can be realized in simple physical systems such as solid-state single photon emitters. As an example, we show how nitrogen-vacancy color centers in diamond can be used to implement the protocol, using the nuclear and electronic spin to form the two qubits.

We present a new approach to path integral Monte Carlo (PIMC) simulations based on the worm algorithm, originally developed for lattice models and extended here to continuous-space many-body systems. The scheme allows for efficient computation of thermodynamic properties, including winding numbers and off-diagonal correlations, for systems of much greater size than that accessible to conventional PIMC simulations. As an illustrative application of the method, we simulate the superfluid transition of ${}^4\mathrm{He}$ in two dimensions.

We consider disordered models of pinning of directed polymers on a defect line, including $(1+1)$-dimensional interface wetting models, disordered Poland-Scheraga models of DNA denaturation, and other $(1+d)$-dimensional polymers in interaction with columnar defects. We consider also random copolymers at a selective interface. These models are known to have a (de)pinning transition at some critical line in the phase diagram. In this work we prove that, as soon as disorder is present, the transition is at least of second order: the free energy is differentiable at the critical line, and the order parameter (contact fraction) vanishes continuously at the transition. On the other hand, it is known that the corresponding nondisordered models can have a first order (de)pinning transition, with a jump in the order parameter. Our results confirm predictions based on the Harris criterion.

We study the motion of an overdamped colloidal particle in a time-dependent nonharmonic potential. We demonstrate the first lawlike balance between applied work, exchanged heat, and internal energy on the level of a single trajectory. The observed distribution of applied work is distinctly non-Gaussian in good agreement with numerical calculations. Both the Jarzynski relation and a detailed fluctuation theorem are verified with good accuracy.

We consider the problem of discriminating between states of a specified set with maximum confidence. For a set of linearly independent states unambiguous discrimination is possible if we allow for the possibility of an inconclusive result. For linearly dependent sets an analogous measurement is one which allows us to be as confident as possible that when a given state is identified on the basis of the measurement result, it is indeed the correct state.

We study rf spectroscopy of ultracold Fermi gas by going beyond the linear response in the field-matter interaction. Higher order perturbation theory allows virtual processes and energy conservation beyond the single-particle level. We formulate an effective higher order theory, which agrees quantitatively with experiments on the pairing gap and is consistent with the absence of the mean-field shift in the spin-flip experiment.

To increase dramatically the distance and the secure key generation rate of quantum key distribution (QKD), the idea of quantum decoys—signals of different intensities—has recently been proposed. Here, we present the first experimental implementation of decoy state QKD. By making simple modifications to a commercial quantum key distribution system, we show that a secure key generation rate of $165\mathrm{\text{bit}}/\mathrm{s}$, which is $1/4$ of the theoretical limit, can be obtained over 15 km of a telecommunication fiber. We also show that with the same experimental parameters, not even a single bit of secure key can be extracted with a non-decoy-state protocol. Compared to building single photon sources, decoy state QKD is a much simpler method for increasing the distance and key generation rate of unconditionally secure QKD.

States with private correlations but little or no distillable entanglement were recently reported. Here, we consider the secure distribution of such states, i.e., the situation when an adversary gives two parties such states and they have to verify privacy. We present a protocol which enables the parties to extract from such untrusted states an arbitrarily long and secure key, even though the amount of distillable entanglement of the untrusted states can be arbitrarily small.

Strongly interacting bosons in a two-dimensional rotating square lattice are investigated via a modified Bose-Hubbard Hamiltonian. Such a system corresponds to a rotating lattice potential imprinted on a trapped Bose-Einstein condensate. Second-order quantum phase transitions between states of different symmetries are observed at discrete rotation rates. For the square lattice we study, there are four possible ground-state symmetries.

We present generic Bell inequalities for multipartite arbitrary dimensional systems. The inequalities that any local realistic theory must obey are violated by quantum mechanics for even dimensional systems. A large set of variants are shown to naturally emerge from the generic Bell inequalities. We discuss particular variants of Bell inequalities that are violated for all the systems including odd dimensional systems.

Can entanglement and the quantum behavior in physical systems survive at arbitrary high temperatures? In this Letter we show that this is the case for a electromagnetic field mode in an optical cavity with a movable mirror in a thermal state. We also identify two different dynamical regimes of generation of entanglement separated by a critical coupling strength.