We discuss a hybrid quantum system where a dielectric membrane situated inside an optical cavity is coupled to a distant atomic ensemble trapped in an optical lattice. The coupling is mediated by the exchange of sideband photons of the lattice laser, and is enhanced by the cavity finesse as well as the square root of the number of atoms. In addition to observing coherent dynamics between the two systems, one can also switch on a tailored dissipation by laser cooling the atoms, thereby allowing for sympathetic cooling of the membrane. The resulting cooling scheme does not require resolved sideband conditions for the cavity, which relaxes a constraint present in standard optomechanical cavity cooling. We present a quantum mechanical treatment of this modular open system which takes into account the dominant imperfections, and identify optimal operation points for both coherent dynamics and sympathetic cooling. In particular, we find that ground state cooling of a cryogenically precooled membrane is possible for realistic parameters.

Quantum steering inequalities allow to demonstrate the presence of entanglement between two parties when one of the two measurement devices is not trusted. Here we show that quantum steering can be demonstrated for an arbitrary low detection efficiency by using two-qubit non-maximally-entangled states. Our result can have important applications in one-sided device-independent quantum key distribution.

We propose to create pairs of semifluxons starting from a flat-phase state in long, optical 0-$\pi$-0 Josephson junctions formed with internal electronic states of atomic Bose-Einstein condensates. In this optical system, we can dynamically tune the length $a$ of the $\pi$ junction, the detuning $\delta$ of the optical transition, or the strength ${\Omega }_0$ of the laser coupling to induce transitions from the flat-phase state to such a semifluxon-pair state. Similarly as in superconducting 0-$\pi$-0 junctions, there are two, energetically degenerate semifluxon-pair states. A linear mean-field model with two internal electronic states explains this degeneracy and shows the distinct static field configuration in a phase diagram of the junction parameters. This optical system offers the possibility to dynamically create a coherent superposition of the distinct semifluxon-pair states and observe macroscopic quantum oscillation.

The complementarity of a single photon's particlelike and wavelike behaviors can be described by the inequality $D^2+V^2\le 1$, with $D$ being the path distinguishability and $V$ being the fringe visibility. In this paper, we generalize this duality relation to the multiphoton case, where two concepts, higher-order distinguishability and higher-order fringe visibility, are introduced to quantify the higher-order particlelike and wavelike behaviors of multiphotons.

Robust and reliable method for reconstructing quasidistributions of integrated intensities of twin beams generated in spontaneous parametric down conversion and entangled in photon numbers is suggested. It utilizes the first and second photocount moments and minimizes the declination from experimental photocount histograms. Qualitatively, different forms of quasidistributions for quantum and classical states are suggested in the method. The transition from quantum to classical states caused by an increased detection noise is discussed. Momentum criterion for nonclassicality of twin beams is suggested.

The quantum predictions for a single nonrelativistic spin-1/2 particle can be reproduced by noncontextual hidden variables. Here we show that quantum contextuality for a relativistic electron moving in a Coulomb potential naturally emerges if relativistic effects are taken into account. The contextuality can be identified through the violation of noncontextuality inequalities. We also discuss quantum contextuality for the free Dirac electron as well as the relativistic Dirac oscillator.

We propose a quantum optical implementation of a class of dissipative spin systems, including the $XXZ$ and Ising model, with ultracold atoms in optical lattices. By employing the motional degree of freedom of the atoms and detuned Raman transitions, we show how to obtain engineerable dissipation and a tunable transversal magnetic field, enabling the study of the dynamics and steady-states of dissipative spin models. As an example of effects made accessible this way, we consider small spin chains and weak dissipation and show by numerical simulation that steady-state expectation values display pronounced peaks at certain critical system parameters. We show that this effect is related to degeneracies in the Hamiltonian and derive a sufficient condition for its occurrence.

Nonlocal properties of ensembles of quantum gates induced by the Haar measure on the unitary group are investigated. We analyze the entropy of entanglement of a unitary matrix $U$ equal to the Shannon entropy of the vector of singular values of the reshuffled matrix. Averaging the entropy over the Haar measure on $U\left(N^2\right)$ we find its asymptotic behavior. For two-qubit quantum gates we derive the induced probability distribution of the interaction content and show that the relative volume of the set of perfect entanglers reads $8/3\pi \approx 0.85$. We establish explicit conditions under which a given one-qubit bistochastic map is unistochastic, so it can be obtained by partial trace over a one-qubit environment initially prepared in the maximally mixed state.

Channel-state duality refers to the correspondence between quantum channels and bipartite states, and it is extremely useful and fruitful in quantum information theory. It is often called the Jamiołkowski isomorphism, the Jamiołkowski-Choi isomorphism, or the Choi-Jamiołkowski isomorphism. We trace the original roots of this duality from a historic perspective, clarify the somewhat misleading term “isomorphism,” reveal the underlying subtle nature, and highlight the seemingly similar but actually different features of the original correspondences in the manner of Pillis, Jamiołkowski, and Choi that lead to the duality. We further illustrate some fundamental properties and diverse applications.

Ionicioiu and Spiller [Phys. Rev. A 85, 062313 (2012)] have recently presented an axiomatic framework for mapping graphs to quantum states of a suitable physical system. Based on their study, we first extend the axiomatic framework to hypergraphs by means of modifying its axioms and consistency conditions. Then we use the axiomatic approach to encode hypergraphs into a different family of quantum states, called the hypergraph states. Moreover, we also try to do the following: (i) show that real equally weighted states, which occur in Grover and Deutsch-Jozsa algorithms, are equivalent to hypergraph states; (ii) describe the relations among hypergraph states, graph states, and stabilizer states; (iii) provide some transformation rules, stated in purely hypergraph theoretical terms, which completely characterize the evolution of hypergraph states under some local operations, including operators in the Pauli group and some special local Pauli measurements; and (iv) investigate some properties of multipartite entanglement of hypergraph states by hypergraph theory.

We investigate the non-Markovian dynamics of quantum correlation between two initially entangled nitrogen-vacancy centers (NVCs) embedded in photonic-crystal cavities (PCCs). We find that a finite quantum correlation is preserved even asymptotically when the transition frequency of the NVC is within the band gap of the PCC, which is quantitatively different from the result of approaching zero under the Born-Markovian approximation. In addition, once the transition frequency of NVC is far beyond the band gap of the PCC, the quantum correlation initially prepared in NVC will be fully transferred to the reservoirs in the long-time limit. Our result reveals that the interplay between the non-Markovian effect of the structured reservoirs and the existence of emitter-field bound state plays an essential role in such quantum correlation preservation. This feature may open new perspectives for devising active decoherence-immune solid-state optical devices.

Subtracting photons from a two-mode squeezed state is a well-known method to increase entanglement. We analyze different strategies of local photon subtraction from a two-mode squeezed state in terms of entanglement gain and success probability. We develop a general framework that incorporates imperfections and losses in all stages of the process: before, during, and after subtraction. By combining all three effects into a single efficiency parameter, we provide analytical and numerical results for subtraction strategies using photon-number-resolving and threshold detectors. We compare the entanglement gain afforded by symmetric and asymmetric subtraction scenarios across the two modes. For a given amount of loss, we identify an optimized set of parameters, such as initial squeezing and subtraction beam splitter transmissivity, that maximize the entanglement gain rate. We identify regimes for which asymmetric subtraction of different Fock states on the two modes outperforms symmetric strategies. In the lossless limit, subtracting a single photon from one mode always produces the highest entanglement gain rate. In the lossy case, the optimal strategy depends strongly on the losses on each mode individually, such that there is no general optimal strategy. Rather, taking losses on each mode as the only input parameters, we can identify the optimal subtraction strategy and required beam splitter transmissivities and initial squeezing parameter. Finally, we discuss the implications of our results for the distillation of continuous-variable quantum entanglement.

With the aid of a quantum memory, the uncertainty about the measurement outcomes of two incompatible observables of a quantum system can be reduced. We investigate this measurement uncertainty bound by considering an additional quantum system connected with both the quantum memory and the measured quantum system. We find that the reduction of the uncertainty bound induced by a quantum memory, on the other hand, implies it is increasing for a third participant. We also show that the properties of the uncertainty bound can be viewed from perspectives of both quantum and classical correlations, in particular, that the behavior of the uncertainty bound is a result of competitions of various correlations between different parties.

Unitary control and decoherence appear to be irreconcilable in quantum mechanics. When a quantum system interacts with an environment, control strategies usually fail due to decoherence. In this article we implement a time-optimal unitary control protocol suitable for quantum open systems. The method is based on successive diabatic and sudden switch transitions in the avoided crossings of the energy spectra of closed systems. We show that the speed of this control protocol meets the fundamental bounds imposed by the quantum speed limit, thus making this scheme ideal for application where decoherence needs to be avoided. We show that this method can achieve complex control strategies with high accuracy in quantum open systems.

Recently, there has been considerable interest in investigating quantum entanglement in two-electron systems, such as two-electron model atoms and quantum dots. In this work, the quantum entanglement of the helium atom and helium-like ions are explored using the two-electron wave functions constructed by the $B$-spline basis. As a measure of the spatial entanglement, the linear entropy of the reduced density matrix is investigated for the ground state and the singlet excited $1sn{s}^{1}S$ states, with $n=2$–10, of the helium atom. The variation of the spatial entanglement with the nuclear charges $Z=2$–15 for the helium-like ions is reported. Results are compared with the existing predictions.

We study the interplay between forgetful and memory-keeping evolution enforced on a two-level system by a multi-spin environment whose elements are coupled to local bosonic baths. Contrarily to the expectation that any non-Markovian effect would be buried by the forgetful mechanism induced by the spin-bath coupling, one can actually induce a full Markovian–to–non-Markovian transition of the two-level system's dynamics, controllable by parameters such as the mismatch between the energy of the two-level system and of the spin environment. For a symmetric coupling, the amount of non-Markovianity surprisingly grows with the number of decoherence channels.

We calculate the increase in the number of modes (the Kac number) per unit length and the change in the zero-point energy (the Casimir energy) of the electromagnetic field resulting from the introduction of a thin, perfectly conducting cylindrical shell of elliptical cross section. Along the way we give a route to the calculation of these physical quantities. The Casimir energy is found to be attractive with the circular case corresponding to the energy maximum and the large eccentricity limit being the divergent energy minimum. As a result, with only Casimir stresses present, a fixed-area shell is unstable and might collapse onto itself. This instability is argued to persist at arbitrary temperature.

We performed high-resolution Fourier-transform spectroscopy measurements and direct-potential-fit of the shelflike RbCs $\left(4\right){}^1{\Sigma }^{+}$ state. Overall, 2317 rovibronic $v^{\prime },J^{\prime }$ term values with $v^{\prime }\in [3,88]$, $J^{\prime }\in [7,276]$ were obtained with accuracy 0.01 cm${}^{-1}$ from the $\left(4\right){}^1{\Sigma }^{+}\to X{}^1{\Sigma }^{+},a{}^3{\Sigma }^{+}$ laser-induced fluorescence (LIF) spectra. The mass-invariant potential energy curve constructed by means of the Chebyshev polynomial expansion reproduced the experimental term values of both ${}^{85}$Rb${}^{133}$Cs and ${}^{87}$Rb${}^{133}$Cs isotopologues with a standard deviation of 0.005 cm${}^{-1}$. We simulated the optical cycle $X{}^1{\Sigma }^{+},a{}^3{\Sigma }^{+}(v^{\prime \prime },J^{\prime \prime }=0)\to \left(4\right){}^1{\Sigma }^{+}(v^{\prime },J^{\prime }=1)\to X{}^1{\Sigma }^{+}(v^{\prime \prime }=0,J^{\prime \prime }=0)$ appropriate to transfer translationally ultracold RbCs molecules into their absolute ground state from the weakly bound rovibronic levels of both singlet $X{}^1{\Sigma }^{+}$ and triplet $a{}^3{\Sigma }^{+}$ ground states. The optimal transfer via the intermediate $\left(4\right){}^1{\Sigma }^{+}$ state with $v^{\prime }=58,60$, and 61 for ${}^{85}$Rb${}^{133}$Cs as well as $v^{\prime }=59$ and 61 for ${}^{87}$Rb${}^{133}$Cs was predicted. The required spin-allowed $\left(4\right){}^1{\Sigma }^{+}-X{}^1{\Sigma }^{+}$ and spin-forbidden $\left(4\right){}^1{\Sigma }^{+}-a{}^3{\Sigma }^{+}$ dipole transition moments were obtained within the framework of ab initio quasirelativistic calculations. The predicted $\left(4\right){}^1{\Sigma }^{+}\to X{}^1{\Sigma }^{+},a{}^3{\Sigma }^{+}$ transition probabilities were consistent with the experimental relative intensity distributions for several $\left(4\right){}^1{\Sigma }^{+}\left(v^{\prime }\right)\to X,a\left(v^{\prime \prime }\right)$ LIF progressions.

We report on the anomalously high line strength of a single rotational level in the ultracold photoassociation of two ${}^{85}$Rb atoms to form ${}^{85}$Rb${}_2$. The $v^{\prime }=111$, $J^{\prime }=5$ level belongs to the Hund's case (c) $2\left(0_g^{+}\right)$ state, which correlates to the Hund's case (a) $2{}^1{\Sigma }_g^{+}$ state. Its strength is caused by coupling with a very near-resonant long-range state. The long-range component is the energetically degenerate $v^{\prime }=155$, $J^{\prime }=5$ level of the case (c) $2\left(1_g\right)$ state, correlating to the case (a) $1{}^1{\Pi }_g$ state. The line strength is enhanced by an order of magnitude through this coupling, relative to nearby vibrational levels and even to nearby rotational levels of the same vibrational level. This enhancement is in addition to the enhancement seen in all $J^{\prime }=3$ and 5 levels of the $2\left(0_g^{+}\right)$ state due to an $l=4$ shape resonance in the $a{}^3{\Sigma }_u^{+}$ state continuum, which alters the distribution of levels formed by photoassociation.