We determine the conditions under which superfluidity with and without quantized vortices appears in a weakly interacting two-component atomic Fermi gas that is trapped in a rotating cylindrical symmetric harmonic potential. We compute the phase diagram as a function of rotation frequency, scattering length, temperature, total number of trapped atoms, and population imbalance. Our analysis is based on solving the Bogoliubov–de Gennes equation.

We consider spin-$1/2$ Fermi gases in arbitrary, integer, or noninteger spatial dimensions, interacting via a Dirac $\delta$ potential. We first generalize the method of Tan's distributions and implement short-range boundary conditions to arbitrary dimension and we obtain a set of universal relations for the Fermi gas. Three-dimensional scattering under very general conditions of transversal confinement is described by an effectively reduced-dimensional scattering length, which we show depends on the three-dimensional scattering length in a universal way. Our formula for noninteger dimensions interpolates between the known results in integer dimensions 1, 2, and 3. Without any need to solve the associated multichannel scattering problem, we find that confinement-induced resonances occur in all dimensions different from $D=2$, while reduced-dimensional contacts, related to the tails of the momentum distributions, are connected to the three-dimensional contact by a correction factor of purely geometric origin.

We derive the stochastic master equations, that is to say, quantum filters, and master equations for an arbitrary quantum system probed by a continuous-mode bosonic input field in two types of nonclassical states. Specifically, we consider the cases where the state of the input field is a superposition or combination of (1) a continuous-mode, single-photon wave packet and vacuum, and (2) any continuous-mode coherent states.

We develop a technique for generating multiphoton nonclassical states via interference between coherent and Fock states using quantum catalysis. By modulating the coherent field strength, the number of catalyst photons, and the ratio of the beam splitter upon which they interfere, a wide range of nonclassical phenomena can be created, including squeezing of up to 1.25 dB, antibunched and superbunched photon statistics, and states exhibiting over 90$\%$ fidelity to displaced coherent superposition states. We perform quantum catalysis experimentally, showing tunability into the nonclassical regime. Our protocol is not limited by weak nonlinearities that underlie most known strategies of preparing multiphoton nonclassical states. Successive iterations of this protocol can lead to direct control over the weights of higher-order terms in the Fock basis, paving the way towards conditional preparation of “designer” multiphoton states for applications in quantum computation, communication, and metrology.

We theoretically analyze the dynamical evolution of photonic quantum walks on Möbius strips and other exotic structures in three-dimensional integrated photonics. Our flexible design allows discrete observations of continuous-time quantum walks of photons in a variety of waveguide arrays. Furthermore, our design allows one to inject photons during the evolution, allowing the possibility of interacting with the photons as they are “walking.” We find that nontrivial array topologies introduce time-dependent symmetries of the two-photon correlations. These properties allow a large degree of control for quantum state engineering of multimode entangled states in these devices.

We investigate the effects of disorder on single-particle time evolution and two-particle correlations in an array of evanescently coupled waveguides with position-dependent tunneling rates. In the clean limit, the energy spectrum of such an array is widely tunable. In the presence of a Hermitian on-site or tunneling disorder, we find that the localization of a wave packet is highly sensitive to this energy spectrum. In particular, for an input confined to a single waveguide, we show that the fraction of light localized to the original waveguide depends on the tunneling profile. We compare the two-particle intensity correlations in the presence of Hermitian tunneling disorder and non-Hermitian, parity- and time-reversal ($\mathcal{PT}$) symmetric, on-site potential disorder. We show the two-particle correlation function in both cases is qualitatively similar since both disorders preserve the particle-hole symmetric nature of the energy spectrum.

The time-energy entanglement of down-converted photon pairs is particularly difficult to characterize because direct measurements of photon arrival times are limited by the temporal resolution of photon detection. Here, we explore an alternative possibility of characterizing the temporal coherence of two-photon wave functions using single-photon interference with weak coherent light. Specifically, this method makes use of the fact that down conversion generates a coherent superposition of vacuum and two-photon states, so that the coincidence count rates for photon pairs after interference with weak coherent light are given by a superposition of the two-photon wave function from the down conversion with the product wave function defined by the weak coherent references. By observing the frequency-dependent interference pattern, it is possible to reconstruct the amplitudes and the phases of the two-photon wave function within the bandwidth of the reference pulses used in the single-photon interferences. The correlated single-photon interferences therefore provide a direct map of the entangled two-photon wave function generated in the down-conversion process.

We outline two general classes of examples of $\mathbb{P}\mathbb{T}$-symmetric quantum Liouvillian dynamics of open many-qubit systems, namely, interacting hard-core bosons (or more general $XYZ$-type spin-1/2 systems) having either (i) pure dephasing noise or (ii) solely single-particle (spin) injection (absorption) incoherent processes. The concept of $\mathbb{P}\mathbb{T}$ symmetry is defined following Prosen [Phys. Rev. Lett. 109, 090404 (2012)] as a formal quantum Liouville-space analog of the parity-time $\mathcal{PT}$ symmetry used in nonconservative classical systems with symmetrically distributed gain and loss.

Although noncommutativity of a certain set of quantum operators (e.g., creation and annihilation operators and Pauli spin operators) has been shown experimentally in recent years, the commutation relation for the position and the momentum operators has not been directly demonstrated to date. In this paper we propose and analyze an experimental scheme for directly observing the noncommutativity of the position and the momentum operators using single-photon quantum interference. While the scheme is studied for the single-photon state as the input quantum state, the analysis applies equally to matter-wave interference, allowing a direct test of the position-momentum commutation relation with a massive particle.

The behavior under particle loss of entanglement and nonlocality is investigated in multipartite quantum systems. In particular, we define a notion of persistency of nonlocality, which leads to device-independent tests of persistent entanglement. We investigate the persistency of various classes of multipartite quantum states, exhibiting a variety of different behaviors. A particular attention is devoted to states featuring maximal persistency. Finally we discuss a link between the symmetry of a state and its persistency, illustrating the fact that too much symmetry reduces the strength of correlations among subsystems. These ideas also lead to a device-independent estimation of the asymmetry of a quantum state.

Topological quantum error-correction codes have high thresholds and are well suited to physical implementation. The minimum-weight perfect-matching algorithm can be used to efficiently handle errors in such codes. We perform a timing analysis of our current implementation of the minimum-weight perfect-matching algorithm. Our implementation performs the classical processing associated with an $n\times n$ lattice of qubits realizing a square surface code storing a single logical qubit of information in a fault-tolerant manner. We empirically demonstrate that our implementation requires only $O\left(n^2\right)$ average time per round of error correction for code distances ranging from 4 to 512 and a range of depolarizing error rates. We also describe tests we have performed to verify that it always obtains a true minimum-weight perfect matching.

An experiment is described that studies electron collisions with laser-excited atoms inside a resonant optical enhancement cavity. A confocal cavity is used to significantly increase the laser power at the interaction region, so that experiments become possible with low-power continuous-wave lasers, particularly at blue and UV wavelengths. The increased power inside the cavity allows previously inaccessible targets and states to be investigated. The method is tested using superelastic scattering experiments from laser-excited calcium at 423 nm for an electron energy of 45 eV, and data are presented at 100 eV using the enhancement cavity.

The application of optical lattices allows a tuning of the geometry of Bose-Einstein condensates to effectively reduced dimensions. In the context of solid-state physics the consideration of the low-dimensional Fröhlich polaron results in an extension of the polaronic strong coupling regime. With this motivation we apply the Jensen-Feynman variational principle to calculate the ground-state properties of the polaron consisting of an impurity in a Bose-Einstein condensate in reduced dimensions. Also the response of this system to Bragg scattering is calculated. We show that reducing the dimension leads to a larger amplitude of the polaronic features and is expected to facilitate the experimental observation of polaronic properties. In optical lattices not only Feshbach resonances but also confinement-induced resonances can be used to tune the polaronic coupling strength. This opens up the possibility to experimentally reveal the intermediate and strong polaronic coupling regimes and resolve outstanding theoretical questions regarding polaron theory.

The polarization states of lasers are crucial issues both for practical applications and fundamental research. In general, they depend in a combined manner on the properties of the gain material and on the structure of the electromagnetic modes. In this paper, we address this issue in the case of solid-state organic lasers, a technology which enables one to vary independently gain and mode properties. Different kinds of resonators are investigated: in-plane microresonators with Fabry-Perot, square, pentagon, stadium, disk, and kite shapes, and external vertical resonators. The degree of polarization $P$ is measured in each case. It is shown that although transverse electric modes prevail generally ($P$ > 0), the kite-shaped microlaser generates negative values for $P$ (i.e., a flip of the dominant polarization which becomes mostly transverse magnetic polarized). In general, we demonstrate that both the pump polarization and the resonator geometry can be used to tailor the polarization of organic lasers. With this aim in view, we, at last, investigate two other degrees of freedom, namely upon using resonant energy transfer and upon pumping the laser dye to a higher excited state. We then demonstrate that significantly lower $P$ factors can be obtained.

A class of experiments is proposed which involve multiple measurements combined with multiple perturbations of a nonlinear classical complex system. A family of multipoint $n+m-1$ dimensional measures $R^{(n,m)}$ that provide complementary information on complex systems is obtained by combining $m$ nonlinear stimuli and $n$ measurements. They represent the combined effect of causal response and noncausal spontaneous fluctuations. The proposed signals can be measured either in the frequency domain or in the time domain. Generalized fluctuation-dissipation relations which hold in the nonlinear regime restrict the number of independent techniques. Two-dimensional correlation plots derived from such measurements can reveal various types of couplings among collective modes.

The decoherence of a two-state tunneling molecule, such as a chiral molecule or ammonia, due to collisions with a buffer gas is analyzed in terms of a succession of quantum states of the molecule satisfying the conditions for a consistent family of histories. With $\hslash \omega$ the separation in energy of the levels in the isolated molecule and $\gamma$ a decoherence rate proportional to the rate of collisions, we find for $\gamma \gg \omega$ (strong decoherence) a consistent family in which the molecule flips randomly back and forth between the left- and right-handed chiral states in a stationary Markov process. For $\gamma <\omega$ there is a family in which the molecule oscillates continuously between the different chiral states, but with occasional random changes of phase, at a frequency that goes to zero at a phase transition $\gamma =\omega$. This transition is similar to the behavior of the inversion frequency of ammonia with increasing pressure, but will be difficult to observe in chiral molecules such as D${}_2$S${}_2$. There are additional consistent families both for $\gamma >\omega$ and for $\gamma <\omega$. In addition, we relate the speed with which chiral information is transferred to the environment to the rate of decrease of complementary types of information (e.g., parity information) remaining in the molecule itself.

Device-independent dimension witnesses provide a lower bound on the dimensionality of classical and quantum systems in a “black box”scenario where only correlations between preparations, measurements, and outcomes are considered. We address the problem of the robustness of dimension witnesses, namely that to witness the dimension of a system or to discriminate between its quantum or classical nature, even in the presence of loss. We consider the case when shared randomness is allowed between preparations and measurements and provide a threshold in the detection efficiency such that dimension witnessing can still be performed.

The adiabatic theory of ionization of an electron, initially bound in a three-dimensional potential well, by an intense low-frequency laser pulse is developed. The general case of arbitrary time dependence and polarization of the laser field and arbitrary potential which can model an atom or a molecule in the single-active-electron approximation is treated, with the only restriction that the potential should not have a Coulomb tail. The asymptotics of the solution to the time-dependent Schrödinger equation and photoelectron momentum distribution in the adiabatic regime are obtained. Both the adiabatic and the rescattering parts of the wave function and ionization amplitude are considered. These asymptotics are expressed in terms of the Siegert state originating from the initial bound state in the presence of a static electric field and scattering states in the unperturbed potential. They are uniform in terms of the amplitude of the laser field and apply to weak underbarrier as well as strong overbarrier fields, provided the condition defining the region of validity of the adiabatic approximation is fulfilled. The theory is illustrated by calculations which confirm that the adiabatic results converge to the exact ones as the adiabatic parameter tends to zero.

A free-oscillation interferometer uses atoms confined in a harmonic trap. Bragg scattering from an off-resonant laser is used to split an atomic wave function into two separated packets. After one or more oscillations in the trap, the wave packets are recombined by a second application of the Bragg laser to close the interferometer. Anharmonicity in the trap potential can lead to a phase shift in the interferometer output. In this paper, analytical expressions for the anharmonic phase are derived at leading order for perturbations of arbitrary power in the position coordinate. The phase generally depends on the initial position and velocity of the atom, which are themselves typically uncertain. This leads to degradation in the interferometer performance, and can be expected to limit the use of a centimeter-scale device to interaction times of about 0.1 s. Methods to improve performance are discussed.

In this paper, we apply the technique of back-action cooling to investigate the effects of both optical and mechanical nonlinearities in optomechanical cooling systems. It is shown that cooling of the nanomechanical oscillator to its ground state is limited by the effects of these nonlinearities. The qualitative result is justified quantitatively by comparing, for the same parameters, our analytical minimum phonon number with the experimental one.