We measure the modification of the transmission spectra of cold ${}^{87}\mathrm{Rb}$ atoms in the proximity of an optical nanofiber (ONF). Van der Waals interactions between the atoms an the ONF surface decrease the resonance frequency of atoms closer to the surface. An asymmetric spectra of the atoms holds information of their spatial distribution around the ONF. We use a far-detuned laser beam coupled to the ONF to thermally excite atoms at the ONF surface. We study the change of transmission spectrum of these atoms as a function of heating laser power. A semiclassical phenomenological model for the thermal excitation of atoms in the atom-surface van der Waals bound states is in good agreement with the measurements. This result suggests that van der Waals potentials could be used to trap and probe atoms at few nanometers from a dielectric surface, a key tool for hybrid photonic-atomic quantum systems.

$\mathcal{PT}$-symmetric quantum mechanics allows finding stationary states in mean-field systems with balanced gain and loss of particles. In this work we apply this method to rotating Bose-Einstein condensates with contact interaction which are known to support ground states with vortices. Due to the particle exchange with the environment transport phenomena through ultracold gases with vortices can be studied. We find that even strongly interacting rotating systems support stable $\mathcal{PT}$-symmetric ground states, sustaining a current parallel and perpendicular to the vortex cores. The vortices move through the nonuniform particle density and leave or enter the condensate through its borders creating the required net current.

We demonstrate that a Kalman filter applied to estimate the position of an optically levitated nanoparticle, and operated in real-time within a field programmable gate array, is sufficient to perform closed-loop parametric feedback cooling of the center-of-mass motion to sub-Kelvin temperatures. The translational center-of-mass motion along the optical axis of the trapped nanoparticle has been cooled by 3 orders of magnitude, from a temperature of 300 K to a temperature of $162\pm 15$ mK.

Quantum systems are affected by interactions with their environments, causing decoherence through two processes: pure dephasing and energy relaxation. For quantum information processing it is important to increase the coherence time of Josephson qubits and other artificial two-level atoms. We show theoretically that if the coupling between these qubits and a cavity field is longitudinal and in the ultrastrong-coupling regime, the system is strongly protected against relaxation. Vice versa, if the coupling is transverse and in the ultrastrong-coupling regime, the system is protected against pure dephasing. Taking advantage of the relaxation suppression, we show that it is possible to enhance their coherence time and use these qubits as quantum memories. Indeed, to preserve the coherence from pure dephasing, we prove that it is possible to apply dynamical decoupling. We also use an auxiliary atomic level to store and retrieve quantum information.

We propose an approach based on a local Hilbert transform to design non-Hermitian potentials generating arbitrary vector fields of directionality, $\vec{p}\left(\vec{r}\right)$, with desired shapes and topologies. We derive a local Hilbert transform to systematically build such potentials by modifying background potentials (being either regular or random, extended or localized). We explore particular directionality fields, for instance in the form of a focus to create sinks for probe fields (which could help to increase absorption at the sink), or to generate vortices in the probe fields. Physically, the proposed directionality fields provide a flexible mechanism for dynamical shaping and precise control over probe fields leading to novel effects in wave dynamics.

We present and analyze a protocol in which polaritons in a noncoplanar optical cavity form fractional quantum Hall states. We model the formation of these states and present techniques for subsequently creating anyons and measuring their fractional exchange statistics. In this protocol, we use a rapid adiabatic passage scheme to sequentially add polaritons to the system, such that the system is coherently driven from $n$- to ($n+1$)-particle Laughlin states. Quasiholes are created by slowly moving local pinning potentials in from outside the cloud. They are braided by dragging the pinning centers around one another, and the resulting phases are measured interferometrically. The most technically challenging issue with implementing our procedure is that maintaining adiabaticity and coherence requires that the two-particle interaction energy $V_0$ be sufficiently large compared to the single-polariton decay rate $\gamma , V_0/\gamma \gg 10N^{2}lnN$, where $N$ is the number of particles in the target state. While this condition is very demanding for present-day experiments where $V_0/\gamma \sim 50$, our protocol presents a significant advance over the existing protocols in the literature.

In an interesting article [Phys. Rev. A 81, 052341 (2010)], Das and Agarwal have discussed the preservation of bipartite entanglement in three-level atoms employing the coherences induced by spontaneous emission. The authors considered various initially entangled qubits prepared from two $\mathsf{V}$-type three-level atoms and showed that more than $50\%$ of the initial (bipartite) entanglement can be preserved in steady state due to vacuum-induced coherence. In this Comment, we point out that their analytical formulas for the entanglement measure contain errors affecting all the numerical results of that article. We substantiate our claim by giving correct analytical results for the time evolution of the two-atom system.

In a recent Comment Nair and Arun, Phys. Rev. A 97, 036301 (2018), it was concluded that the two-qubit entanglement protection reported in our work [Das and Agarwal, Phys. Rev. A 81, 052341 (2010)] is erroneous. While we acknowledge the error in analytical results on concurrence when dipole matrix elements were unequal, the essential conclusions on entanglement protection are not affected.

Quantum theory does not provide a unique definition for the joint probability of two noncommuting observables, which is the next important question after the Born's probability for a single observable. Instead, various definitions were suggested, e.g., via quasiprobabilities or via hidden-variable theories. After reviewing open issues of the joint probability, we relate it to quantum imprecise probabilities, which are noncontextual and are consistent with all constraints expected from a quantum probability. We study two noncommuting observables in a two-dimensional Hilbert space and show that there is no precise joint probability that applies for any quantum state and is consistent with imprecise probabilities. This contrasts with theorems by Bell and Kochen-Specker that exclude joint probabilities for more than two noncommuting observables, in Hilbert space with dimension larger than two. If measurement contexts are included into the definition, joint probabilities are not excluded anymore, but they are still constrained by imprecise probabilities.

Theories with indefinite causal structure have been studied from both the fundamental perspective of quantum gravity and the practical perspective of information processing. In this paper we point out a restriction in forming tensor products of objects with indefinite causal structure in certain models: there exist both classical and quantum objects the tensor products of which violate the normalization condition of probabilities, if all local operations are allowed. We obtain a necessary and sufficient condition for when such unrestricted tensor products of multipartite objects are (in)valid. This poses a challenge to extending communication theory to indefinite causal structures, as the tensor product is the fundamental ingredient in the asymptotic setting of communication theory. We discuss a few options to evade this issue. In particular, we show that the sequential asymptotic setting does not suffer the violation of normalization.

We present a technique to coarse grain quantum states in a finite-dimensional Hilbert space. Our method is distinguished from other approaches by not relying on structures such as a preferred factorization of Hilbert space or a preferred set of operators (local or otherwise) in an associated algebra. Rather, we use the data corresponding to a given set of states, either specified independently or constructed from a single state evolving in time. Our technique is based on principle component analysis (PCA), and the resulting coarse-grained quantum states live in a lower-dimensional Hilbert space whose basis is defined using the underlying (isometric embedding) transformation of the set of fine-grained states we wish to coarse grain. Physically, the transformation can be interpreted to be an “entanglement coarse-graining” scheme that retains most of the global, useful entanglement structure of each state, while needing fewer degrees of freedom for its reconstruction. This scheme could be useful for efficiently describing collections of states whose number is much smaller than the dimension of Hilbert space, or a single state evolving over time.

The lifetime of the long-lived $5d{}^2{D}_{5/2}$ level in ${}^{138}\mathrm{Ba}^{+}$ ions was measured in trapped single ions and small ion crystals using continuous quantum jump spectroscopy. We find ${\tau }_{D_{5/2}}=25.6\left(0.5\right)\text{s}$, significantly below previously reported values. We have verified our result by exploiting camera images of the stored ions, which enabled monitoring the cleanliness and sufficiently low temperature of the ion samples, and investigating common systematic effects.

The development of quantum technologies which use quantum states of the light field interacting with other systems creates a demand for such states over wide frequency ranges. In this work we compare the bipartite entanglement and Einstein-Podolsky-Rosen (EPR) -steering properties of the two different parametric schemes which produce third-harmonic optical fields from an input field at the fundamental frequency. The first scheme uses second harmonic cascaded with sum-frequency generation, while the second uses triply degenerate four- wave mixing, also known as direct third-harmonic generation. We find that both schemes produce continuous-variable bipartite entanglement and EPR steering over a frequency range which has previously been unobtainable. The direct scheme produces a greater degree of EPR steering, while the cascaded scheme allows for greater flexibility in having three available bipartitions, thus allowing for greater flexibility in the tailoring of light matter interfaces. There are also parameter regimes in both for which classical mean-field analyses fail to predict the mean-field solutions. Both schemes may be very useful for applications in quantum communication and computation networks, as well as providing for quantum interfaces between a wider range of light and atomic ensembles than is presently practicable.

We report on the observation of subharmonic resonances in high-order wave mixing associated with the quantized vibrational levels of atoms trapped in a one-dimensional optical lattice created by two intense nearly counterpropagating coupling beams. These subharmonic resonances, occurring at $\pm 1/2$ and $\pm 1/3$ of the frequency separation between adjacent vibrational levels, are observed through phase-match angularly resolved six- and eight-wave mixing processes. We investigate how these resonances evolve with the intensity of the incident probe beam, which couples with one of the coupling beams to create anharmonic coherence gratings between adjacent vibrational levels. Our experimental results also show evidence of high-order processes associated with coherence involving nonadjacent vibrational levels. Moreover, we also demonstrate that these induced high-order coherences can be stored in the medium and the associated optical information retrieved after a controlled storage time.

The effects of Lorentz boosts on the quantum entanglement encoded by a pair of massive spin-$\frac{1}{2}$ particles are described according to the Lorentz covariant structure described by Dirac bispinors. The quantum system considered incorporates four degrees of freedom: two of them related to the bispinor intrinsic parity and the other two related to the bispinor spin projection, i.e., the Dirac particle helicity. Because of the natural multipartite structure involved, the Meyer-Wallach global measure of entanglement is preliminarily used for computing global quantum correlations, while the entanglement separately encoded by spin degrees of freedom is measured through the negativity of the reduced two-particle spin-spin state. A general framework to compute the changes on quantum entanglement induced by a boost is developed and then specialized to describe three particular antisymmetric two-particle states. According to the results obtained, two-particle spin-spin entanglement cannot be created by the action of a Lorentz boost in a spin-spin separable antisymmetric state. On the other hand, the maximal spin-spin entanglement encoded by antisymmetric superpositions is degraded by Lorentz boosts driven by high-speed frame transformations. Finally, the effects of boosts on chiral states are shown to exhibit interesting invariance properties, which can only be obtained through such a Lorentz covariant formulation of the problem.

Quantum steering is one form of quantum correlations interpolating between entanglement and Bell nonlocality, which in some cases can be detected by various steering inequalities. Recently, a remarkable and useful steerability criterion via geometric Bell-like inequalities was established [M. Zukowski, A. Dutta, and Z. Yin, Phys. Rev. A 91, 032107 (2015)]. We report an experimental investigation of this steering criterion and verify the geometric Bell-like steering inequality experimentally by using of the Werner states. The results demonstrate that the geometric Bell-like steering inequality is a convenient tool to detect quantum steering both theoretically and practically.

There are heuristic arguments proposing that the accuracy of monitoring position of a free mass $m$ is limited by the standard quantum limit (SQL): ${\sigma }^2(X\left(t\right))\ge {\sigma }^2(X\left(0\right))+(t^2/m^2){\sigma }^2(P\left(0\right))\ge \hslash t/m$, where ${\sigma }^2(X\left(t\right))$ and ${\sigma }^2(P\left(t\right))$ denote variances of the Heisenberg representation position and momentum operators. Yuen [Phys. Rev. Lett. 51, 719 (1983)] discovered that there are contractive states for which this result is incorrect. Here I prove universally valid rigorous quantum limits (RQL), viz. rigorous upper and lower bounds on ${\sigma }^2(X\left(t\right))$ in terms of ${\sigma }^2(X\left(0\right))$ and ${\sigma }^2(P\left(0\right))$, given by Eq. (12) for a free mass and by Eq. (36) for an oscillator. I also obtain the maximally contractive and maximally expanding states which saturate the RQL, and use the contractive states to set up an Ozawa-type measurement theory with accuracies respecting the RQL but beating the standard quantum limit. The contractive states for oscillators improve on the Schrödinger coherent states of constant variance and may be useful for gravitational wave detection and optical communication.

We investigate the dynamical properties for non-Hermitian triple-well systems with a loss in the middle well. When chemical potentials in the two end wells are uniform and nonlinear interactions are neglected, there always exists a dark state whose eigenenergy becomes zero and the projections onto which do not change over time and the loss factor. The increasing of the loss factor only makes the damping form from the oscillating decay to the overdamping decay. However, when the nonlinear interaction is introduced, even interactions in the two end wells are also uniform, and the projection of the dark state will be obviously diminished. Simultaneously, the increasing of the loss factor will also aggravate the loss. In this process, the interaction in the middle well plays no role. When two chemical potentials or interactions in the two end wells are not uniform, all disappear with time. In addition, when we extend the triple-well system to a general $(2n+1)$ well, the loss is greatly reduced by the factor $1/2n$ in the absence of the nonlinear interaction.

In all practical communication channels, the code word consists of Gaussian states and the measurement strategy is often a Gaussian detector such as homodyning or heterodyning. We investigate the communication performance using a phase-conjugated alphabet and joint Gaussian detection in a phase-insensitive amplifying channel. We find that a communication scheme consisting of a phase-conjugating alphabet of coherent states and a joint detection strategy significantly outperforms a standard coherent-state strategy based in individual detection. Moreover, we show that the performance can be further enhanced by using entanglement and that the performance is completely independent of the gain of the phase-insensitively amplifying channel.