The time-dependent Gross-Pitaevskii equation describes the dynamics of initially trapped Bose-Einstein condensates. We present a rigorous proof of this fact starting from a many-body bosonic Schrödinger equation with a short-scale repulsive interaction in the dilute limit. Our proof shows the persistence of an explicit short-scale correlation structure in the condensate.

Over 8 months, we monitored transition frequencies between nearly degenerate, opposite-parity levels in two isotopes of atomic dysprosium (Dy). These frequencies are sensitive to variation of the fine-structure constant ($\alpha$) due to relativistic corrections of opposite sign for the opposite-parity levels. In this unique system, in contrast to atomic-clock comparisons, the difference of the electronic energies of the opposite-parity levels can be monitored directly utilizing a rf electric-dipole transition between them. Our measurements show that the frequency variation of the 3.1-MHz transition in ${}^{163}\mathrm{Dy}$ and the 235-MHz transition in ${}^{162}\mathrm{Dy}$ are $9.0\pm 6.7\mathrm{Hz}/\mathrm{yr}$ and $-0.6\pm 6.5\mathrm{Hz}/\mathrm{yr}$, respectively. These results provide a rate of fractional variation of $\alpha$ of $(-2.7\pm 2.6)\times {10}^{-15}{\mathrm{yr}}^{-1}$ ($1\sigma$) without assumptions on constancy of other fundamental constants, indicating absence of significant variation at the present level of sensitivity.

Given an initial quantum state $|{\psi }_I⟩$ and a final quantum state $|{\psi }_F⟩$, there exist Hamiltonians $H$ under which $|{\psi }_I⟩$ evolves into $|{\psi }_F⟩$. Consider the following quantum brachistochrone problem: subject to the constraint that the difference between the largest and smallest eigenvalues of $H$ is held fixed, which $H$ achieves this transformation in the least time $\tau$? For Hermitian Hamiltonians $\tau$ has a nonzero lower bound. However, among non-Hermitian $\mathcal{P}\mathcal{T}$-symmetric Hamiltonians satisfying the same energy constraint, $\tau$ can be made arbitrarily small without violating the time-energy uncertainty principle. This is because for such Hamiltonians the path from $|{\psi }_I⟩$ to $|{\psi }_F⟩$ can be made short. The mechanism described here is similar to that in general relativity in which the distance between two space-time points can be made small if they are connected by a wormhole. This result may have applications in quantum computing.

Coherence properties of Bose-Einstein condensates offer the potential for improved interferometric phase contrast. However, decoherence effects due to the mean-field interaction shorten the coherence time, thus limiting potential sensitivity. In this work, we demonstrate increased coherence times with number squeezed states in an optical lattice using the decay of Bloch oscillations to probe the coherence time. We extend coherence times by a factor of 2 over those expected with coherent state Bose-Einstein condensate interferometry. We observe quantitative agreement with theory both for the degree of initial number squeezing as well as for prolonged coherence times.

We analyze the problem of a quantum computer in a correlated environment protected from decoherence by quantum error correction using a perturbative renormalization group approach. The scaling equation obtained reflects the competition between the dimension of the computer and the scaling dimension of the correlations. For an irrelevant flow, the error probability is reduced to a stochastic form for a long time and/or a large number of qubits; thus, the traditional derivation of the threshold theorem holds for these error models. In this way, the “threshold theorem” of quantum computing is rephrased as a dimensional criterion.

We report on precision measurements of the frequency of the radial compression mode in a strongly interacting, optically trapped Fermi gas of ${}^6\mathrm{Li}$ atoms. Our results allow for a test of theoretical predictions for the equation of state in the BEC-BCS crossover. We confirm recent quantum Monte Carlo results and rule out simple mean-field BCS theory. Our results show the long-sought beyond-mean-field effects in the strongly interacting Bose-Einstein condensation (BEC) regime.

A novel transport phenomenon is identified that is induced by inertial Brownian particles which move in simple one-dimensional, symmetric periodic potentials under the influence of both a time periodic and a constant, biasing driving force. Within tailored parameter regimes, thermal equilibrium fluctuations induce the phenomenon of absolute negative mobility (ANM), which means that the particle noisily moves backwards against a small constant bias. When no thermal fluctuations act, the transport vanishes identically in these tailored regimes. ANM can also occur in the absence of fluctuations on grounds which are rooted solely in the complex, inertial deterministic dynamics. The experimental verification of this new transport scheme is elucidated for the archetype symmetric physical system: a convenient setup consisting of a resistively and capacitively shunted Josephson junction device.

For a second-order phase transition the critical energy range of interest is larger than the energy range covered by a canonical Monte Carlo simulation at the critical temperature. Such an extended energy range can be covered by performing a Wang-Landau recursion for the spectral density followed by a multicanonical simulation with fixed weights. But in the conventional approach one loses the advantage due to cluster algorithms. A cluster version of the Wang-Landau recursion together with a subsequent multibondic simulation improves for 2D and 3D Ising models the efficiency of the conventional Wang-Landau or multicanonical approach by power laws in the lattice size. In our simulations real gains in CPU time reach 2 orders of magnitude.

We show how stationary entanglement between an optical cavity field mode and a macroscopic vibrating mirror can be generated by means of radiation pressure. We also show how the generated optomechanical entanglement can be quantified, and we suggest an experimental readout scheme to fully characterize the entangled state. Surprisingly, such optomechanical entanglement is shown to persist for environment temperatures above 20 K using state-of-the-art experimental parameters.

We study Bose-Einstein condensates with purely dipolar interactions in oblate traps. We find that the condensate always becomes unstable to collapse when the number of particles is sufficiently large. We analyze the instability, and find that it is the trapped-gas analogue of the “roton-maxon” instability previously reported for a gas that is unconfined in 2D. In addition, we find that under certain circumstances the condensate wave function attains a biconcave shape, with its maximum density away from the center of the gas. These biconcave condensates become unstable due to azimuthal excitation—an angular roton.

We measure the relative phase of two Bose-Einstein condensates confined in a radio frequency induced double-well potential on an atom chip. We observe phase coherence between the separated condensates for times up to $\sim 200\mathrm{ms}$ after splitting, a factor of 10 longer than the phase diffusion time expected for a coherent state for our experimental conditions. The enhanced coherence time is attributed to number squeezing of the initial state by a factor of 10. In addition, we demonstrate a rotationally sensitive (Sagnac) geometry for a guided atom interferometer by propagating the split condensates.

An intercept-resend attack on a continuous-variable quantum-key-distribution protocol is investigated experimentally. By varying the interception fraction, one can implement a family of attacks where the eavesdropper totally controls the channel parameters. In general, such attacks add excess noise in the channel, and may also result in non-Gaussian output distributions. We implement and characterize the measurements needed to detect these attacks, and evaluate experimentally the information rates available to the legitimate users and the eavesdropper. The results are consistent with the optimality of Gaussian attacks resulting from the security proofs.

The Luther-Emery liquid is a state of matter that is predicted to occur in one-dimensional systems of interacting fermions and is characterized by a gapless charge spectrum and a gapped spin spectrum. In this Letter we discuss a realization of the Luther-Emery phase in a trapped cold-atom gas. We study by means of the density-matrix renormalization-group technique a two-component atomic Fermi gas with attractive interactions subject to parabolic trapping inside an optical lattice. We demonstrate how this system exhibits compound phases characterized by the coexistence of spin pairing and atomic-density waves. A smooth crossover occurs with increasing magnitude of the atom-atom attraction to a state in which tightly bound spin-singlet dimers occupy the center of the trap. The existence of atomic-density waves could be detected in the elastic contribution to the light-scattering diffraction pattern.

Evaporative cooling was performed to cool fermionic ${}^{173}\mathrm{Yb}$ atoms in a crossed optical dipole trap. The large elastic collision rate leads to efficient evaporation and we have successfully cooled the atoms to $0.37\pm 0.06$ of the Fermi temperature, that is to say, to a quantum degenerate regime. In this regime, a plunge of evaporation efficiency was observed as a result of Fermi degeneracy.

We report on the adiabatic splitting of a Bose-Einstein condensate of ${}^{87}\mathrm{Rb}$ atoms by an asymmetric double-well potential located above the edge of a perpendicularly magnetized TbGdFeCo film atom chip. By controlling the barrier height and double-well asymmetry, the sensitivity of the axial splitting process is investigated through observation of the fractional atom distribution between the left and right wells. This process constitutes a novel sensor for which we infer a single shot sensitivity to gravity fields of $\delta g/g\approx 2\times {10}^{-4}$. From a simple analytic model, we propose improvements to chip-based gravity detectors using this demonstrated methodology.

For an atomic condensate in an axially symmetric magnetic trap, the sum of the axial components of the orbital angular momentum and the hyperfine spin is conserved. Inside an Ioffe-Pritchard trap (IPT) whose magnetic field ($B$ field) is not axially symmetric, the difference of the two becomes surprisingly conserved. In this Letter we investigate the relationship between the values of the sum or difference angular momentums for an atomic condensate inside a magnetic trap and the associated gauge potential induced by the adiabatic approximation. Our result provides significant new insight into the vorticity of magnetically trapped atomic quantum gases.

We experimentally demonstrate that the entanglement between Gaussian entangled states can be increased by non-Gaussian operations. Coherent subtraction of single photons from Gaussian quadrature-entangled light pulses, created by a nondegenerate parametric amplifier, produces delocalized states with negative Wigner functions and complex structures more entangled than the initial states in terms of negativity. The experimental results are in very good agreement with the theoretical predictions.

We present Monte Carlo simulations of the spanning-forest model ($q\to 0$ limit of the ferromagnetic Potts model) in spatial dimensions $d=3$, 4, 5. We show that, in contrast to the two-dimensional case, the model has a ferromagnetic second-order phase transition at a finite positive value $w_c$. We present numerical estimates of $w_c$ and of the thermal and magnetic critical exponents. We conjecture that the upper critical dimension is 6.

A striking feature of quantum error correcting codes is that they can sometimes be used to correct more errors than they can uniquely identify. Such degenerate codes have long been known, but have remained poorly understood. We provide a heuristic for designing degenerate quantum codes for high noise rates, which is applied to generate codes that can be used to communicate over almost any Pauli channel at rates that are impossible for a nondegenerate code. The gap between nondegenerate and degenerate code performance is quite large, in contrast to the tiny magnitude of the only previous demonstration of this effect. We also identify a channel for which none of our codes outperform the best nondegenerate code and show that it is nevertheless quite unlike any channel for which nondegenerate codes are known to be optimal.

Shot noise in a voltage source changes the character of the quantum (dissipative) phase transition in an ultrasmall Josephson junction: The superconductor-insulator transition transforms into the superconductor-metal transition. In the metallic phase, the $IV$ curve probes the voltage distribution generated by shot noise, whereas in the superconducting phase, it probes the counting statistics of electrons traversing the noise junction.