We propose and analyze a general mechanism of disorder-induced order in two-component Bose-Einstein condensates, analogous to corresponding effects established for $XY$ spin models. We show that a random Raman coupling induces a relative phase of $\pi /2$ between the two BECs and that the effect is robust. We demonstrate it in one, two, and three dimensions at $T=0$ and present evidence that it persists at small $T>0$. Applications to phase control in ultracold spinor condensates are discussed.

We consider two-species of fermions in a rotating trap that interact via an $s$-wave Feshbach resonance, at total Landau level filling factor two (or one for each species). We show that the system undergoes a quantum phase transition from a fermion integer quantum Hall state to a boson fractional quantum Hall state as the pairing interaction strength increases, with the transition occurring near the resonance. The effective field theory for the transition is shown to be that of a (emergent) massless relativistic bosonic field coupled to a Chern-Simons gauge field, with the coupling giving rise to semionic statistics to the emergent particles.

Topological order characterizes those phases of matter that defy a description in terms of symmetry and cannot be distinguished in terms of local order parameters. Here we show that a system of $n$ spins forming a lattice on a Riemann surface can undergo a second order quantum phase transition between a spin-polarized phase and a string-net condensed phase. This is an example of a quantum phase transition between magnetic and topological order. We furthermore show how to prepare the topologically ordered phase through adiabatic evolution in a time that is upper bounded by $O(\sqrt{n})$. This provides a physically plausible method for constructing and initializing a topological quantum memory.

We study the nonequilibrium steady state realized in a general stochastic system attached to multiple heat baths. Starting from the detailed fluctuation theorem, we derive concise and suggestive expressions for the corresponding stationary distribution which are correct up to the second order in thermodynamic forces. The probability of a microstate $\eta$ is proportional to $\exp [\Phi (\eta )]$ where $\Phi (\eta )=-\sum _k{\beta }_k{\mathcal{E}}_k(\eta )$ is the excess entropy change. Here, ${\mathcal{E}}_k(\eta )$ is the difference between two kinds of conditioned path ensemble averages of excess heat transfer from the $k$th heat bath whose inverse temperature is ${\beta }_k$. This result can be easily extended to steady states maintained with other sources, e.g., particle current driven by an external force. Our expression may be verified experimentally in nonequilibrium states realized, for example, in mesoscopic systems.

A reasonable physical intuition in the study of interacting quantum systems says that, independent of the initial state, the system will tend to equilibrate. In this work we introduce an experimentally accessible setting where relaxation to a steady state is exact, namely, for the Bose-Hubbard model quenched from a Mott quantum phase to the free strong superfluid regime. We rigorously prove that the evolving state locally relaxes to a steady state with maximum entropy constrained by second moments—thus maximizing the entanglement. Remarkably, for this to be true, no time average is necessary. Our argument includes a central limit theorem and exploits the finite speed of information transfer. We also show that for all periodic initial configurations (charge density waves) the system relaxes locally, and identify experimentally accessible signatures in optical lattices as well as implications for the foundations of statistical mechanics.

We investigate the effect of nonlinearity on beam dynamics in parity-time ($\mathcal{P}\mathcal{T}$) symmetric potentials. We show that a novel class of one- and two-dimensional nonlinear self-trapped modes can exist in optical $\mathcal{P}\mathcal{T}$ synthetic lattices. These solitons are shown to be stable over a wide range of potential parameters. The transverse power flow within these complex solitons is also examined.

We investigate the phase diagram of asymmetric two-component Fermi gases at zero temperature as a function of polarization and interaction strength. The equations of state of the uniform superfluid and normal phase are determined using quantum Monte Carlo simulations. We find three different mixed states, where the superfluid and the normal phase coexist in equilibrium, corresponding to phase separation between (a) the polarized superfluid and the fully polarized normal gas, (b) the polarized superfluid and the partially polarized normal gas, and (c) the unpolarized superfluid and the partially polarized normal gas.

We introduce a general operational characterization of information-preserving structures—encompassing noiseless subsystems, decoherence-free subspaces, pointer bases, and error-correcting codes—by demonstrating that they are isometric to fixed points of unital quantum processes. Using this, we show that every information-preserving structure is a matrix algebra. We further establish a structure theorem for the fixed states and observables of an arbitrary process, which unifies the Schrödinger and Heisenberg pictures, places restrictions on physically allowed kinds of information, and provides an efficient algorithm for finding all noiseless and unitarily noiseless subsystems of the process.

We present a method for determining the free-energy dependence on a selected number of collective variables using an adaptive bias. The formalism provides a unified description which has metadynamics and canonical sampling as limiting cases. Convergence and errors can be rigorously and easily controlled. The parameters of the simulation can be tuned so as to focus the computational effort only on the physically relevant regions of the order parameter space. The algorithm is tested on the reconstruction of an alanine dipeptide free-energy landscape.

A quantum Monte Carlo simulation of a system of bosonic hard rods in one dimension is presented and discussed. The calculation is exact since the analytical form of the wave function is known and is in excellent agreement with predictions obtained from asymptotic expansions valid at large distances. The analysis of the static structure factor and the pair distribution function indicates that a solidlike and a gaslike phases exist at high and low densities, respectively. The one-body density matrix decays following a power law at large distances and produces a divergence in the low density momentum distribution at $k=0$ which can be identified as a quasicondensate.

We show that any two different unitary operations acting on an arbitrary multipartite quantum system can be perfectly distinguished by local operations and classical communication when a finite number of runs is allowed. Intuitively, this result indicates that the lost identity of a nonlocal unitary operation can be recovered locally. No entanglement between distant parties is required.

We derive new duality relations that link the energy of configurations associated with a class of soft pair potentials to the corresponding energy of the dual (Fourier-transformed) potential. We apply them by showing how information about the classical ground states of short-ranged potentials can be used to draw new conclusions about the nature of the ground states of long-ranged potentials and vice versa. They also lead to bounds on the $T=0$ system energies in density intervals of phase coexistence, the identification of a one-dimensional system that exhibits an infinite number of “phase transitions,” and a conjecture regarding the ground states of purely repulsive monotonic potentials.

We present a semidefinite program optimization approach to quantum error correction that yields codes and recovery procedures that are robust against significant variations in the noise channel. Our approach allows us to optimize the encoding, recovery, or both, and is amenable to approximations that significantly improve computational cost while retaining fidelity. We illustrate our theory numerically for optimized 5-qubit codes, using the standard $[5,1,3]$ code as a benchmark. Our optimized encoding and recovery yields fidelities that are uniformly higher by 1–2 orders of magnitude against random unitary weight-2 errors compared to the $[5,1,3]$ code with standard recovery.

Extensions of statistical mechanics are routinely being used to infer free energies from the work performed over single-molecule nonequilibrium trajectories. A key element of this approach is the ubiquitous expression $dW/dt=\partial H(x,t)/\partial t$, which connects the microscopic work $W$ performed by a time-dependent force on the coordinate $x$ with the corresponding Hamiltonian $H(x,t)$ at time $t$. Here we show that this connection, as pivotal as it is, cannot be used to estimate free-energy changes. We discuss the implications of this result for single-molecule experiments and atomistic molecular simulations and point out possible avenues to overcome these limitations.

We analyze the recurrence probability (Pólya number) for $d$-dimensional unbiased quantum walks. A sufficient condition for a quantum walk to be recurrent is derived. As a by-product we find a simple criterion for localization of quantum walks. In contrast with classical walks, where the Pólya number is characteristic for the given dimension, the recurrence probability of a quantum walk depends in general on the topology of the walk, choice of the coin and the initial state. This allows us to change the character of the quantum walk from recurrent to transient by altering the initial state.

In the collision of a high-energy proton beam and a strong laser field, merging of laser photons can occur due to the polarization of vacuum. The probability of photon merging is calculated by exactly accounting for the laser field which involves a highly nonperturbative dependence on the laser intensity and frequency. It is shown that the nonperturbative vacuum-polarization effects can be experimentally measured by combining the next generation of tabletop petawatt lasers with proton accelerators presently available.

The general problem of finding the ground state energy of lattice Hamiltonians is known to be very hard, even for a quantum computer. We show here that this is the case even for translationally invariant systems in 1D. We also show that a quantum computer can be built in a 1D chain with a fixed, translationally invariant Hamitonian consisting of nearest-neighbor interactions only. The result of the computation is obtained after a prescribed time with high probability.

We examine stochastic processes that are used to model nonequilibrium processes (e.g., pulling RNA or dragging colloids) and so deliberately violate detailed balance. We argue that by combining an information-theoretic measure of irreversibility with nonequilibrium work theorems, the thermal physics implied by abstract dynamics can be determined. This measure is bounded above by thermodynamic entropy production and so may quantify how well a stochastic dynamics models reality. We also use our findings to critique various modeling approaches and notions arising in steady-state thermodynamics.

A series of recent articles have presented results demonstrating optical cooling of macroscopic objects, highlighting the importance of this phenomenon for investigations of macroscopic quantum mechanics and its implications for thermal noise in gravitational wave detectors. In this Letter, we present a measurement of the off-resonance suspension thermal noise of a 1 g oscillator, and we show that it can be cooled to just 70 mK. The cooling is achieved by using a servo to impose a phase delay between oscillator motion and optical force. A model is developed to show how optical rigidity and optical cooling can be interchangeable using this technique.

The radio-frequency spectra of ultracold Fermi atoms are calculated by including final-state interactions affecting the excited level of the transition and compared with the experimental data. A competition is revealed between pairing-gap effects which tend to push the oscillator strength toward high frequencies away from threshold and final-state effects which tend instead to pull the oscillator strength toward threshold. As a result of this competition, the position of the peak of the spectra cannot be simply related to the value of the pairing gap, whose extraction thus requires support from theoretical calculations.