The transition from “few to many” has recently been probed experimentally in an ultracold harmonically confined one-dimensional lithium gas, in which a single impurity atom interacts with a background gas consisting of one, two, or more identical fermions [A. N. Wenz et al., Science 342, 457 (2013)]. For repulsive interactions between the background or majority atoms and the impurity, the interaction energy for relatively moderate system sizes was analyzed and found to converge toward the corresponding expression for an infinitely large Fermi gas. Motivated by these experimental results, we apply perturbative techniques to determine the interaction energy for weak and strong coupling strengths and derive approximate descriptions for the interaction energy for repulsive interactions with varying strength between the impurity and the majority atoms and any number of majority atoms.

We study a five-level $\text{quasi}-\Lambda$ system of cold atoms for achieving high-order photonic band gaps (PBGs) probed by an ultraviolet field in two cases where either an infrared or a visible control field works in the standing-wave configuration to induce one atomic grating. Transfer-matrix calculations for appropriate rubidium levels demonstrate that three fifth-order band gaps or two second-order band gaps can be generated near the probe resonance when the standing-wave control field is modulated to satisfy relevant Bragg conditions in the regime of electromagnetically induced transparency. These high-order PBGs, as characterized by homogeneous high reflectivities, can be dynamically tuned in positions and widths on demand and may be extended to develop efficient devices (like diodes and reflectors) for manipulating weak high-frequency light with strong low-frequency light.

We theoretically investigate a two-cavity optomechanical system in which a cavity (cavity $a$) couples to a mechanical resonator via radiation pressure and to another cavity (cavity $c$) via a common waveguide. In the excitation of a strong pump filed to cavity $a$, the steady-state entanglement between cavity $a$ and $c$, as a quantum channel, can be generated, which provides an indirect optical pathway to excite cavity $c$ by means of the pump filed. Quantum interference between the direct and indirect optical pathways gives rise to an optomechanically induced transparency appearing in the probe transmission of cavity $c$. Unlike in a typical optomechanically induced transparency effect, the electromagnetical control of the transmission is implemented by resorting to the quantum channel. Furthermore, the coupling strength of the two cavities is an important factor of the quantum channel, which can influence the width of the transparency window and the bistable behavior of the mean photon number in cavity $a$. We also illustrate that the electromagnetical control via quantum channel can be exploited to implement the optical switch and the slow light.

We obtained a propagation equation for an optical pulse at an electromagnetically induced transparency window guided on a gas-filled hollow-core photonic crystal fiber. This equation admits dissipative solitons whose analytical expression was also obtained. Depending on the parameter region, they may be stable or unstable. We simulated a typical experimental arrangement and found some cases for which the equation parameters are such that it admits stable solitons.

We present a theoretical model of photon counting measurements on conditionally generated narrowband single-photon states that are produced via cavity-enhanced spontaneous parametric down-conversion, then frequency up-converted from the telecom wavelength of 1550 nm to the visible wavelength of 532 nm. The highly nonclassical character of the up-converted states is certified by a quantum non-Gaussianity witness that is determined from coincidence measurements with single-photon detectors in a Hanbury-Brown–Twiss configuration. We find our model in good agreement with the experimental data, and we investigate a useful effect caused by the dead time of the trigger detector, whose clicks herald conditional preparation of the single-photon state. Due to the dead time, a click of the trigger detector excludes the possibility of a trigger event at a certain preceding time interval, during which the measured idler beam is thus projected onto a vacuum state. Due to quantum correlations between signal and idler beams, this reduces the multiphoton contributions in the conditionally generated state of the signal beam and accordingly increases the value of the quantum non-Gaussianity witness. We also show that spurious heralding detections due to after-pulsing can be suppressed by accepting a click of the trigger detector only if its distance from a previous click of this detector exceeds a certain suitably chosen threshold.

It is found that the measurement disturbance relation (MDR) determines the strength of quantum correlation and hence is one of the essential facets of the nature of quantum nonlocality. In reverse, the exact form of MDR may be ascertained through measuring the correlation function. To this aim, an optical experimental scheme is proposed. Moreover, by virtue of the correlation function, we find that the quantum entanglement, the quantum nonlocality, and the uncertainty principle can be explicitly correlated.

We report measurements of the absolute excitation frequencies of ${}^{165}\mathrm{Ho}$ $4f^{11}6sns$ and $4f^{11}6snd$ odd-parity Rydberg series. The states are detected through depletion of a magneto-optical trap via a two-photon excitation scheme. Measurements of 162 Rydberg levels in the range $n=40$–101 yield quantum defects well described by the Rydberg-Ritz formula. We observe a strong perturbation in the $ns$ series around $n=51$ due to an unidentified interloper at 48515.47(4) ${\mathrm{cm}}^{-1}$. From the series convergence, we determine the first ionization potential $E_{\mathrm{IP}}=48565.910\left(3\right)$ ${\mathrm{cm}}^{-1}$, which is three orders of magnitude more accurate than previous work. This work is an important step towards using Ho atoms for collective encoding of a quantum register.

We investigate the dynamics of a homogenous Bose-Einstein condensate (BEC) following a sudden quench of the scattering length. Our focus is the time evolution of short-range correlations via the dynamical contact. We compute the dynamics using a combination of two- and many-body models and we propose an intuitive connection between them that unifies their short-time, short-range predictions. Our two-body models are exactly solvable and, when properly calibrated, lead to analytic formulas for the contact dynamics. Immediately after the quench, the contact exhibits strong oscillations at the frequency of the two-body bound state. These oscillations are large in amplitude and their time average is typically much larger than the Bogoliubov prediction. The condensate fraction shows similar oscillations, whose amplitude we are able to estimate. These results demonstrate the importance of including the bound state in descriptions of diabatically quenched BEC experiments.

Although a number of measures for quantum non-Markovianity have been proposed recently, it is still an open question whether these measures directly characterize the memory effect of the environment, i.e., the dependence of a quantum state on its past in a time evolution. In this paper, we present a criterion and propose a measure for non-Markovianity with clear physical interpretations of the memory effect. The non-Markovianity is defined by the inequality $T(t_2,t_0)\ne T(t_2,t_1)T(t_1,t_0)$ in terms of memoryless dynamical map $T$ introduced in this paper. This definition is conceptually distinct from that based on divisibility used by Rivas et al. [Phys. Rev. Lett. 105, 050403 (2010)], whose violation is manifested by noncomplete positivity of the dynamical map. We demonstrate via a typical quantum process that without Markovian approximation, nonzero memory effects (non-Markovianity) always exist even if the non-Markovianity is zero by the other non-Markovianity measures.

All classical and quantum technologies that encode in and retrieve information from optical fields rely on the ability to selectively manipulate orthogonal field modes of light. Such manipulation can be achieved with high selectivity for polarization modes and transverse-spatial modes. For the time-frequency degree of freedom, this could efficiently be achieved for a limited choice of approximately orthogonal modes, i.e., nonoverlapping bins in time or frequency. We recently proposed a method that surmounts the selectivity barrier for sorting arbitrary orthogonal temporal modes [Opt. Lett. 39, 2924 (2014).] using cascaded interferometric quantum frequency conversion in nonlinear optical media. We call this method temporal-mode interferometry, as it has a close resemblance to the well-known separated-fields atomic interferometry method introduced by Ramsey. The method has important implications for quantum memories, quantum dense coding, quantum teleportation, and quantum key distribution. Here we explore the inner workings of the method in detail, and extend it to multiple stages with a concurrent asymptotic convergence of temporal-mode selectivity to unity. We also complete our analysis of pump-chirp compensation to counter pump-induced nonlinear phase modulation in four-wave mixing implementations.

Characterizing noisy quantum processes is important to quantum computation and communication (QCC), since quantum systems are generally open. To date, all methods of characterization of quantum dynamics (CQD), typically implemented by quantum process tomography, are off-line, i.e., QCC and CQD are not concurrent, as they require distinct state preparations. Here we introduce a method, “quantum error correction based characterization of dynamics,” in which the initial state is any element from the code space of a quantum error correcting code that can protect the state from arbitrary errors acting on the subsytem subjected to unknown dynamics. The statistics of stabilizer measurements, with possible unitary preprocessing operations, are used to characterize the noise, while the observed syndrome can be used to correct the noisy state. Our method requires at most $2(4^n-1)$ configurations to characterize arbitrary noise acting on $n$ qubits.

We analyze sound waves (phonons, i.e. Bogoliubov excitations) propagating on continuous-wave (cw) solutions of repulsive $F=1$ spinor Bose-Einstein condensates (BECs) such as ${}^{23}\mathrm{Na}$ (which is antiferromagnetic or polar) and ${}^{87}\mathrm{Rb}$ (which is ferromagnetic). Zeeman splitting by a uniform magnetic field is included. All cw solutions to ferromagnetic BECs with vanishing $M_F=0$ particle density and nonzero components in both $M_F=\pm 1$ fields are subject to modulational instability (MI). Modulational instability increases with increasing particle density. Modulational instability also increases with differences in the components' wave numbers; this effect is larger at lower densities but becomes insignificant at higher particle densities. Continuous-wave solutions to antiferromagnetic (polar) BECs with vanishing $M_F=0$ particle density and nonzero components in both $M_F=\pm 1$ fields do not suffer MI if the wave numbers of the components are the same. If there is a wave-number difference, MI initially increases with increasing particle density and then peaks before dropping to zero beyond a given particle density. The cw solutions with particles in both $M_F=\pm 1$ components and nonvanishing $M_F=0$ components do not have MI if the wave numbers of the components are the same, but do exhibit MI when the wave numbers are different. Direct numerical simulations of a continuous wave with weak white noise confirm that weak noise grows fastest at wave numbers with the largest MI and show some of the results beyond small-amplitude perturbations. Phonon dispersion curves are computed numerically; we find analytic solutions for the phonon dispersion in a variety of limiting cases.

Ground-state cooling of mesoscopic mechanical resonators is a fundamental requirement for testing of quantum theory and for implementation of quantum information. We analyze the cavity optomechanical cooling limits in the intermediate coupling regime, where the light-enhanced optomechanical coupling strength is comparable with the cavity decay rate. It is found that in this regime the cooling breaks through the limits in both the strong-coupling and the weak-coupling regimes. The lowest cooling limit is derived analytically under the optimal conditions of cavity decay rate and coupling strength. In essence, cooling to the quantum ground state requires $Q_{\mathrm{m}}>2.4n_{\mathrm{th}}$, with $Q_{\mathrm{m}}$ being the mechanical quality factor and $n_{\mathrm{th}}$ being the thermal phonon number. Remarkably, ground-state cooling is achievable starting from room temperature, when the mechanical $Q$-frequency product $Q_{\mathrm{m}}{\nu }_{\mathrm{m}}>1.5\times {10}^{13}$ Hz and both the cavity decay rate and the coupling strength exceed the thermal decoherence rate. Our study provides a general framework for optimizing the backaction cooling of mesoscopic mechanical resonators.

We demonstrate quantum bath engineering for preparation of any orbital state with the controllable phase factor of a superconducting flux qubit assisted by a microwave coplanar waveguide resonator. We investigate the polarization efficiency of the arbitrary direction rotating on the Bloch sphere, and obtain an effective Rabi frequency by using the convergence condition of the Markovian master equation. The processes of polarization can be implemented effectively in a dissipative environment created by resonator photon loss when the spectrum of the microwave resonator matches with the specially tailored Rabi and resonant frequencies of the drive. Our calculations indicate that state-preparation fidelities in excess of 99% and the required time on the order of magnitude of a microsecond are in principle possible for experimentally reasonable sample parameters. Furthermore, our proposal could be applied to other systems with spin-based qubits.

We construct a nonequilibrium theory for the dynamics of two interacting finite-temperature atomic Bose-Einstein condensates and use it to numerically estimate the relative rates of the arising collisional processes near equilbrium. The condensates are described by dissipative Gross-Pitaevskii equations, coupled to quantum Boltzmann equations for the thermal atoms. The density-density interactions between atoms in different components facilitate a number of transport processes of relevance to sympathetic cooling: in particular, considering realistic miscible and immiscible trapped atomic ${}^{87}\mathrm{Rb}\text{−}{}^{41}\mathrm{K}$ and ${}^{87}\mathrm{Rb}\text{−}{}^{85}\mathrm{Rb}$ condensate mixtures, we highlight the dominance of an intercomponent scattering process associated with collisional “exchange” of condensed and thermal atoms between the components close to equilibrium.

We establish a quantitative relation between Hardy's paradox and the breaking of the uncertainty principle in the sense of measurement-disturbance relations in the conditional measurement of noncommuting operators. The analysis of the inconsistency of local realism with entanglement by Hardy is simplified if this breaking of measurement-disturbance relations is taken into account, and a much simplified experimental test of local realism is illustrated in the framework of Hardy's thought experiment. The essence of Hardy's model is identified as a combination of two conditional measurements, which give rise to definite eigenvalues to two noncommuting operators simultaneously in hidden-variables models. Better understanding of the intimate interplay of entanglement and measurement disturbance is crucial in the current discussions of Hardy's paradox using the idea of weak measurement, which is based on a general analysis of measurement-disturbance relations.

The Clauser-Horne-Shimony-Holt inequality applies when measurements with binary outcomes are performed on physical systems under the assumption of local realism. Testing such inequalities in the quantum realm usually involves either measurements of two-valued quantum observables or predefining a context-dependent binning procedure. Here we establish the conditions to test the Clauser-Horne-Shimony-Holt inequality using any quantum observable. Our result applies to observables with an arbitrary spectrum, and no prior knowledge of their underlying Hilbert space's dimension is required. Finally, we demonstrate the proposed general measurement strategy, that can be seen as positive operator-valued measurements performed on the system, using the formalism of modular variables applied to the transverse degrees of freedom of single photons.

Motivated by very recent experiments, we consider a scenario “à la Bell” in which two protagonists test the Clauser-Horne-Shimony-Holt (CHSH) inequality using a photon-pair source based on spontaneous parametric down conversion and imperfect photon detectors. The conventional wisdom says that (i) if the detectors have unit efficiency, the CHSH violation can reach its maximum quantum value of $2\sqrt{2}$. To obtain the maximal possible violation, it suffices that the source emits (ii) maximally entangled photon pairs (iii) in two well-defined single modes. Through a nonperturabive calculation of nonlocal correlations, we show that none of these statements are true. By providing the optimal pump parameters, measurement settings and state structure for any detection efficiency and dark count probability, our results give the recipe to close all the loopholes in a Bell test using photon pairs.

We derive an upper bound for the distinguishability-based non-Markovianity measure of a two-level system and prove that for certain master equations the exact value of the measure achieves this bound. Furthermore, we obtain an easily calculable lower bound for the divisibility-based non-Markovianity measure of an $n$-level system. We illustrate the calculation of these bounds through examples, considering in detail the spin-boson model. We show that the differences between the two measures in the spin-boson model are caused by the drift vector that is also responsible for the nonunitality of the dynamical map.