One longstanding difficult problem in quantum dissipative dynamics is to solve the spin-boson model in a non-Markovian regime where a tractable systematic master equation does not exist. The spin-boson model is particularly important due to its crucial applications in quantum noise control and manipulation as well as its central role in developing quantum theories of open systems. Here we solve this important model by developing a non-Markovian quantum Langevin approach. By projecting the quantum Langevin equation onto the coherent states of the bath, we can derive a set of non-Markovian quantum Bloch equations containing no explicit noise variables. This special feature offers a tremendous advantage over the existing stochastic Schrödinger equations in numerical simulations. The physical significance and generality of our approach are briefly discussed.

High-dimensional quantum entanglement is drawing attention because it enables us to perform quantum information tasks that are robust against noises. To test the nonlocality of entangled qudits, the Collins-Gisin-Linden-Massar-Popescu (CGLMP) inequality has been proposed and demonstrated using qudits based on orbital angular momentum, time-energy uncertainty, and frequency bins. Here, we report the generation and observation of time-bin entangled ququarts. We implemented a measurement for the CGLMP inequality test using cascaded delay Mach-Zehnder interferometers fabricated by using planar light-wave circuit technology, with which we achieved a precise and stable measurement for time-bin-entangled ququarts. In addition, we generated an optimized entangled state by modulating the pump pulse intensities, with which we can observe the theoretical maximum violation for the CGLMP inequality test. As a result, we successfully observed a Bell-type parameter $S_4=2.774\pm 0.025$ violating the CGLMP inequality for the maximally entangled state and an enhanced Bell-type parameter $S_4=2.913\pm 0.023$ for the optimized entangled state.

We consider a Dirac one-electron atom placed in a weak, static, uniform magnetic field. We show that, to the first order in the strength $B$ of the external field, the only electric multipole moments, which are induced by the perturbation in the atom, are those of an even order. Using the Sturmian expansion of the generalized Dirac-Coulomb Green function [R. Szmytkowski, J. Phys. B 30, 825 (1997); J. Phys. B 30, 2747 (1997)], We derive a closed-form expression for the electric quadrupole moment induced in the atom in an arbitrary discrete energy eigenstate. The result, which has the form of a double finite sum involving the generalized hypergeometric functions ${}_3{F}_2$ of the unit argument, agrees with the earlier relativistic formula for that quantity, obtained by us for the ground state of the atom.

We calculate and analyze Feshbach resonance spectra for ultracold $\mathrm{Yb}\left({}^1{S}_0\right)+\mathrm{Yb}\left({}^3{P}_2\right)$ collisions as a function of an interatomic potential scaling factor $\lambda$ and external magnetic field. We show that, at zero field, the resonances are distributed randomly in $\lambda$, but that signatures of quantum chaos emerge as a field is applied. The random zero-field distribution arises from superposition of structured spectra associated with individual total angular momenta. In addition, we show that the resonances with respect to magnetic field in the experimentally accessible range of 400 to 2000 G are chaotically distributed, with strong level repulsion that is characteristic of quantum chaos.

In recent experiments bosonic [Atala et al., Nat. Phys. 10, 588 (2014); Stuhl et al., Science 349, 1514 (2015)] as well as fermionic ladders [Mancini et al. Science  349, 1510 (2015)] with a uniform flux were studied and different interesting many-body states were observed. Motivated by these experiments, we extend the uniform synthetic magnetic field to a periodic case and show that a commensurate synthetic magnetic field offers an alternative scheme to realize topological phases in many-body systems of ultracold Fermi gases in ladderlike optical lattices. Using the exact diagonalization, we numerically determine the topological band structure, edge states, nonzero Chern numbers, Hofstadter-butterfly-like spectrum, and a complete phase diagram of noninteracting fermionic ladders.

Vortex lattices in rapidly rotating Bose-Einstein condensates lead to a periodic modulation of the superfluid density with a triangular symmetry. Here we show that this symmetry can be combined with an external perturbation in order to create superlattice structures with two or more periodicities. Considering a condensate that is kicked by an optical lattice potential, we find the appearance of transient moiré lattice structures, which can be identified using the kinetic energy spectrum.

We develop a Gaussian state treatment that allows a transparent quantum description of the continuous, nondestructive imaging of and feedback on a Bose-Einstein condensate. We have previously demonstrated [A. C. J. Wade et al., Phys. Rev. Lett. 115, 060401 (2015)] that the measurement backaction of stroboscopic imaging leads to selective squeezing and entanglement of quantized density oscillations. Here, we investigate how the squeezing and entanglement are affected by the finite spatial resolution and geometry of the probe laser beam and of the detector and how they can be optimized.

We investigate the Rabi oscillation of an atom placed inside a quantum cavity where each mirror is formed by a chain of atoms trapped near a one-dimensional waveguide. This proposal was studied previously with the use of Markov approximation, where the delay due to the finite travel time of light between the two cavity mirrors is neglected. We show that Rabi oscillation analogous to that obtained with high-finesse classical cavities is achieved only when this travel time is much larger than the time scale that characterizes the superradiant response of the mirrors. Therefore, the delay must be taken into account and the dynamics of the problem is inherently non-Markovian. Parameters of interest such as the Rabi frequency and the cavity loss rate due to photon leakage through the mirrors are obtained.

We present a theoretical model for a Kerr-like interaction between two registers of a compound gradient echo memory (GEM). This type of interaction is known to generate cross-phase modulation (XPM) between optical fields, an effect that is limited by the typically small values of nonlinearities in crystals. Here we show that in GEM systems the phase shift increases linearly with the interaction time and quadratically with the strength of the field. Increasing storage (interaction) times would then lead to stronger XPM effects even with fields with very low intensity. This interaction also generates two other effects: entanglement between the registers, which depends on the strength of the interaction and its spatial profile, and an interaction-induced gradient. We show that the latter produces leakage during the storage stage depending on the shape of the stored pulses, an undesirable consequence that can be minimized by carefully designing the temporal profile of the input fields.

We report the observation of quantum reflection from a narrow attractive potential using bright solitary matter waves formed from a ${}^{85}\mathrm{Rb}$ Bose-Einstein condensate. We create the attractive potential using a tightly focused, red-detuned laser beam, and observe reflection of up to 25% of the atoms, along with the confinement of atoms at the position of the beam. We show that the observed reflected fraction is much larger than theoretical predictions for a simple Gaussian potential well. A more detailed model of bright soliton propagation, accounting for the generic presence of small subsidiary intensity maxima in the red-detuned beam, suggests that these small intensity maxima are the cause of this enhanced reflection.

We consider the general problem of estimating an unknown control parameter of an open quantum system. We establish a direct relation between the evolution of both system and environment and the precision with which the parameter can be estimated. We show that when the open quantum system undergoes a first-order dynamical phase transition the quantum Fisher information (QFI), which gives the upper bound on the achievable precision of any measurement of the system and environment, becomes quadratic in observation time (cf. “Heisenberg scaling”). In fact, the QFI is identical to the variance of the dynamical observable that characterizes the phases that coexist at the transition, and enhanced scaling is a consequence of the divergence of the variance of this observable at the transition point. This identification makes it possible to establish the finite time scaling of the QFI. Near the transition the QFI is quadratic in time for times shorter than the correlation time of the dynamics. In the regime of enhanced scaling the optimal measurement whose precision is given by the QFI involves measuring both system and output. As a particular realization of these ideas, we describe a theoretical scheme for quantum enhanced estimation of an optical phase shift using the photons being emitted from a quantum system near the coexistence of dynamical phases with distinct photon emission rates.

We present the amount of information, fidelity, and reversibility obtained by arbitrary quantum measurements on completely unknown states. These quantities are expressed as functions of the singular values of a measurement operator corresponding to the obtained outcome. As an example, we consider a class of quantum measurements with highly degenerate singular values to discuss trade-offs among information, fidelity, and reversibility. The trade-offs are at the level of a single outcome, in the sense that the quantities pertain to each single outcome rather than the average over all possible outcomes.

Here we study multiplayer linear games, a natural generalization of xor games to multiple outcomes. We generalize a recently proposed efficiently computable bound, in terms of the norm of a game matrix, on the quantum value of two-player games to linear games with $n$ players. As an example, we bound the quantum value of a generalization of the well-known CHSH game to $n$ players and $d$ outcomes. We also apply the bound to show in a simple manner that any nontrivial functional box, that could lead to trivialization of communication complexity in a multiparty scenario, cannot be realized in quantum mechanics. We then present a systematic method to derive device-independent witnesses of genuine tripartite entanglement.

We prove that the squared Rényi-$\alpha$ entanglement ($\mathrm{SR}\alpha \mathrm{E}$), which is the generalization of entanglement of formation, obeys a general monogamy inequality in an arbitrary $N$-qubit mixed state. Furthermore, for a class of Rényi-$\alpha$ entanglement, we prove that the monogamy relations of the $\mathrm{SR}\alpha \mathrm{E}$ have a hierarchical structure when the $N$-qubit system is divided into $k$ parties. As a by-product, the analytical relation between the Rényi-$\alpha$ entanglement and the squared concurrence is derived for bipartite $2\otimes d$ systems. Based on the monogamy properties of $\mathrm{SR}\alpha \mathrm{E}$, we can construct the corresponding multipartite entanglement indicators, which still work well even when the indicators based on the squared concurrence and EOF lose their efficacy. In addition, the monogamy property of the $\mu \mathrm{th}$ power of Rényi-$\alpha$ entanglement is analyzed.

The tunneling ionization of an excited hydrogen atom by a static electric field $\mathbf{E}$ is investigated for the case where the initial electron has an orbital angular momentum $\mathbf{L}$ nonparallel to $\mathbf{E}$. The outgoing electron has a nonzero mean transverse velocity $\langle {\mathbf{v}}_{\mathrm{T}}\rangle$ in the direction of $\mathbf{E}\times \langle \mathbf{L}\rangle$. During this process the linear Stark effect makes $\langle \mathbf{L}\rangle$ and $\langle {\mathbf{v}}_{\mathrm{T}}\rangle$ oscillate or rotate about $\mathbf{E}$. Measures of the asymmetry are calculated at leading order in $\mathbf{E}$ for an initial state $2P$ state. The generalization to coherent elliptic Rydberg states is outlined. A subset of these states whose classical Kepler ellipses rotate rigidly about $\mathbf{E}$ is particularly interesting for the observation of the asymmetry. The preparation of states with $\mathbf{L}$ nonparallel to $\mathbf{E}$ and the conditions to get a sizable ${\mathbf{v}}_{\mathrm{T}}$ asymmetry are discussed.

We experimentally determine the equation of state of a laser-cooled gas. By employing the Lane-Emden formalism, widely used in astrophysics, we derive the equilibrium atomic profiles in large magneto-optical traps where the thermodynamic effects are cast in a polytropic equation of state. The effects of multiple scattering of light are included, which results in a generalized Lane-Emden equation for the atomic profiles. A detailed experimental investigation reveals an excellent agreement with the model, with a twofold significance. On one hand, we can infer the details of the equation of state of the system, from an ideal gas to a correlated phase due to an effective electrical charge for the atoms, which is accurately described by a microscopical description of the effective electrostatic interaction. On the other hand, we are able map the effects of multiple scattering onto directly controllable experimental variables, which paves the way to subsequent experimental investigations of this collective interaction.

We theoretically investigate the generation of atom-light entanglement via Raman superradiance in an optical cavity, and show how this can be used to enhance the sensitivity of atom interferometry. We model a realistic optical cavity, and show that by careful temporal shaping of the optical local oscillator used to measure the light emitted from the cavity, information in the optical mode can be combined with the signal from the atom interferometer to reduce the quantum noise, and thus increase the sensitivity. It was found in Phys. Rev. Lett. 110, 053002 (2013) that an atomic “seed” was required in order to reduce spontaneous emission and allow for single mode behavior of the device. In this paper we find that the optical cavity reduces the need for an atomic seed, which allows for stronger atom-light correlations and a greater level of quantum enhancement.

The control of light transmission through a standing-wave Fabry-Pérot cavity containing atoms is theoretically and numerically investigated, when the cavity mode beam and an intersecting control beam are both close to specific atomic resonances. A four-level atomic system is considered and its interaction with the cavity mode is studied by solving for the cavity field and atomic state populations. The conditions for optical bistability of the atom-cavity system are obtained. The response of the intracavity intensity to an intersecting beam on atomic resonance is understood in the presence of stationary atoms (closed system) and nonstatic atoms (open system) in the cavity. The nonstatic system of atoms is modelled by adjusting the atomic state populations to represent the exchange of atoms in the cavity mode, which corresponds to a thermal environment where atoms are moving in and out of the cavity mode volume. The control behavior with three- and two-level atomic systems is also studied, and the rich physics arising out of these systems for closed and open atomic systems is discussed. The solutions to the models are used to interpret the steady-state and transient behavior observed by Sharma et al. [Phys. Rev. A 91, 043824 (2015)].