Extending the single-photon transmission distance is a basic requirement for the implementation of quantum communication on a global scale. In this work we report the single-photon exchange from a medium Earth orbit satellite (MEO) at more than $7000\text{km}$ of slant distance to the ground station at the Matera Laser Ranging Observatory. The single-photon transmitter was realized by exploiting the corner cube retroreflectors mounted on the LAGEOS-2 satellite. Long duration of data collection is possible with such altitude, up to 43 min in a single passage. The mean number of photons per pulse (${\mu }_{\mathrm{sat}}$) has been limited to 1 for 200 s, resulting in an average detection rate of $3.0\text{counts}/\text{s}$ and a signal-to-noise ratio of 1.5. The feasibility of single-photon exchange from MEO satellites paves the way to tests of quantum mechanics in moving frames and to global quantum Information.

Uncertainty principle lies at the heart of quantum mechanics, while nonlocality is an intriguing phenomenon of quantum mechanics to rule out local causal theories. One subtle form of nonlocality is so-called Einstein-Podolsky-Rosen (EPR) steering, which holds the potential for shared entanglement verification even if the one-sided measurement device is untrusted. However, certifying EPR steering remains a big challenge presently. Here, we employ the local uncertainty relation to provide an experimental friendly approach for EPR steering verification. We show that the strength of EPR steering is quantitatively linked to the strength of the uncertainty relation, as well as the amount of entanglement. We find also that the realignment method works for detecting EPR steering of an arbitrary dimensional system.

Tomography of a quantum state is usually based on a positive-operator-valued measure (POVM) and on their experimental statistics. Among the available reconstructions, the maximum-likelihood (MaxLike) technique is an efficient one. We propose an extension of this technique when the measurement process cannot be simply described by an instantaneous POVM. Instead, the tomography relies on a set of quantum trajectories and their measurement records. This model includes the fact that, in practice, each measurement could be corrupted by imperfections and decoherence, and could also be associated with the record of continuous-time signals over a finite amount of time. The goal is then to retrieve the quantum state that was present at the start of this measurement process. The proposed extension relies on an explicit expression of the likelihood function via the effective matrices appearing in quantum smoothing and solutions of the adjoint quantum filter. It allows us to retrieve the initial quantum state as in standard MaxLike tomography, but where the traditional POVM operators are replaced by more general ones that depend on the measurement record of each trajectory. It also provides, aside from the MaxLike estimate of the quantum state, confidence intervals for any observable. Such confidence intervals are derived, as the MaxLike estimate, from an asymptotic expansion of multidimensional Laplace integrals appearing in Bayesian mean estimation. A validation is performed on two sets of experimental data: photon(s) trapped in a microwave cavity subject to quantum nondemolition measurements relying on Rydberg atoms, and heterodyne fluorescence measurements of a superconducting qubit.

We show that trace distance measure of coherence is a strong monotone for all qubit and, so called, $X$ states. An expression for the trace distance coherence for all pure states and a semidefinite program for arbitrary states is provided. We also explore the relation between $l_1$-norm and relative entropy based measures of coherence, and give a sharp inequality connecting the two. In addition, it is shown that both $l_p$-norm- and Schatten-$p$-norm–based measures violate the (strong) monotonicity for all $p\in (1,\infty )$.

We investigate the intermediate permutational symmetries of a system of qubits that lie in between the perfect symmetric and antisymmetric cases. We prove that, on average, pure states of qubits picked at random with respect to the uniform measure on the unit sphere of the Hilbert space are almost as antisymmetric as they are allowed to be. We then observe that multipartite entanglement, measured by the generalized Meyer-Wallach measure, tends to be larger in subspaces that are more antisymmetric than the complete symmetric one. Eventually, we prove that all states contained in the most antisymmetric subspace are relevant multipartite entangled states in the sense that their 1-qubit reduced states are all maximally mixed.

The Born-Oppenheimer approximation leads to the counterintuitive result of a vanishing electronic flux density upon vibrational dynamics in the electronic ground state. To circumvent this long known issue, we propose using pairwise antisymmetrically translated vibronic densities to generate a symmetric electronic density that can be forced to satisfy the continuity equation approximately. The so-called Born-Oppenheimer broken-symmetry ansatz yields all components of the flux density simultaneously while requiring only knowledge about the nuclear quantum dynamics on the electronic adiabatic ground-state potential energy surface. The underlying minimization procedure is transparent and computationally inexpensive, and the solution can be computed from the standard output of any quantum chemistry program. Taylor series expansion reveals that the implicit electron dynamics originates from nonadiabatic coupling to the explicit Born-Oppenheimer nuclear dynamics. Our approach is applied to the ${\mathrm{H}}_2^{+}$ molecular ion vibrating in its ${}^2{\mathrm{\Sigma }}_g^{+}$ ground state. The electronic flux density is found to have the correct nodal structure and symmetry properties at all times.

As dipolar gases become more readily accessible in experiment there is a need to develop a comprehensive theoretical framework of the few-body physics of these systems. Here, we extend the coupled-pair approach developed for the unitary two-component Fermi gas to a few-body system of dipolar bosons in a spherical harmonic trap. The long range and anisotropy of the dipole-dipole interaction is handled by a flexible and efficient correlated Gaussian basis with stochastically variational optimization. Solutions of the two-body problem are used to calculate the eigenenergy spectrum and structural properties of three trapped bosonic dipoles. This demonstrates the efficiency and flexibility of the coupled-pair approach at dealing with systems with complex interactions.

More recently, laser cooling of the diatomic radical magnesium monofluoride (${}^{24}{\mathrm{Mg}}^{19}\mathrm{F}$) is being experimentally preformed [Appl. Phys. Express 8, 092701 (2015) and Opt. Express 22, 28645 (2014)] and was also studied theoretically [Phys. Rev. A 91, 042511 (2015)]. However, some important problems still remain unsolved, so, in our paper, we perform further theoretical study for the feasibility of laser cooling and trapping the ${}^{24}{\mathrm{Mg}}^{19}\mathrm{F}$ molecule. At first, the highly diagonal Franck-Condon factors of the main transitions are verified by the closed-form approximation, Morse approximation, and Rydberg-Klein-Rees inversion methods, respectively. Afterwards, we investigate the lower $X{}^2{\mathrm{\Sigma }}_{1/2}^{+}$ hyperfine manifolds using a quantum effective Hamiltonian approach and obtain the zero-field hyperfine spectrum with an accuracy of less than 30 $\mathrm{kHz}\sim 5\mu \text{K}$ compared with the experimental results, and then find out that one cooling beam and one or two repumping beams with their first-order sidebands are enough to implement an efficient laser slowing and cooling of ${}^{24}{\mathrm{Mg}}^{19}\mathrm{F}$. Meanwhile, we also calculate the accurate hyperfine structure magnetic $g$ factors of the rotational state ($X{}^2{\mathrm{\Sigma }}_{1/2}^{+},N=1$) and briefly discuss the influence of the external fields on the hyperfine structure of ${}^{24}{\mathrm{Mg}}^{19}\mathrm{F}$ as well as its possibility of preparing three-dimensional magneto-optical trapping. Finally we give an explanation for the difference between the Stark and Zeeman effects from the perspective of parity and time reversal symmetry. Our study shows that, besides appropriate excitation wavelengths, the short lifetime for the first excited state $A{}^2{\mathrm{\Pi }}_{1/2}$, and lighter mass, the ${}^{24}{\mathrm{Mg}}^{19}\mathrm{F}$ radical could be a good candidate molecule amenable to laser cooling and magneto-optical trapping.

Studies of atomic systems in electric fields are challenging because of the diverging perturbation series. However, physically meaningful Stark shifts and ionization rates can be found by analytical continuation of the series using appropriate branch cut functions. We apply this approach to low-dimensional hydrogen atoms to study the effects of reduced dimensionality. We find that modifications by the electric field are strongly suppressed in reduced dimensions. This finding is explained from a Landau-type Wentzel–Kramers–Brillouin analysis of the ionization process.

We consider a two-component Fermi gas with attractive interactions on a square optical lattice, and study the interplay of Zeeman field, spin-orbit coupling, and next-nearest-neighbor hopping on the ground-state phase diagrams in the entire BCS-BEC evolution. In particular, we first classify and distinguish all possible superfluid phases by the momentum-space topology of their zero-energy quasiparticle-quasihole excitations, and then numerically establish a plethora of quantum phase transitions in between. These transitions are further signaled and evidenced by the changes in the corresponding topological invariant of the system, i.e., its Chern number. Lastly, we find that the superfluid phase exhibits a reentrant structure, separated by a fingering normal phase, the origin of which is traced back to the changes in the single-particle density of states.

Owing to the use of a symmetrization $\pi$ pulse at the middle of their laser sequences, Mach-Zehnder-type atom interferometers are insensitive to clocks shifts and Doppler shifts, if constant, but to changes in these quantities, which makes them accurate and sensitive inertial-force sensors. However, variations of the Raman laser coupling between laser pulses restore a parasitic sensitivity to the Doppler shift. This effect, which sets a limit to the symmetry of the interferometer, is quantitatively evaluated here as a function of the experimental parameters, in the case of an atom gravimeter experiment, and compared to expectations. We show in particular that velocity-distribution asymmetries lead to parasitic phase shifts that can compromise the accuracy and long-term stability of the gravity measurement in the low ${10}^{-9}g$ range.

We theoretically investigate the uniform spin susceptibility $\chi$ in the superfluid phase of an ultracold Fermi gas in the region of the Bardeen-Cooper-Schrieffer–Bose-Einstein-condensate (BCS-BEC) crossover. In our previous paper [H. Tajima et al., Phys. Rev. A 89, 033617 (2014)], including pairing fluctuations within an extended $T$-matrix approximation (ETMA), we showed that strong pairing fluctuations cause the so-called spin-gap phenomenon, where $\chi$ is anomalously suppressed even in the normal state near the superfluid phase transition temperature $T_{\mathrm{c}}$. In this paper, we extend this work to the superfluid phase below $T_{\mathrm{c}}$, to clarify how this many-body phenomenon is affected by the superfluid order. From the comparison of the ETMA $\chi$ with the Yosida function describing the spin susceptibility in a weak-coupling BCS superfluid, we identify the region where pairing fluctuations crucially affect this magnetic quantity below $T_{\mathrm{c}}$ in the phase diagram with respect to the strength of a pairing interaction and the temperature. This spin-gap regime is found to be consistent with the previous pseudogap regime determined from the pseudogapped density of states. We also compare our results with a recent experiment on a ${}^6\mathrm{Li}$ Fermi gas. Since the spin susceptibility is sensitive to the formation of spin-singlet preformed pairs, our results would be useful for the study of pseudogap physics in an ultracold Fermi gas on the viewpoint of the spin degrees of freedom.

Dipolar bilayers with antiparallel polarization, i.e., opposite polarization in the two layers, exhibit liquidlike rather than gaslike behavior. In particular, even without external pressure, a self-bound liquid droplet of constant density will form. We investigate the symmetric case of two identical layers, corresponding to a two-component Bose system with equal partial densities. The zero-temperature equation of state $E\left(\rho \right)/N$, where $\rho$ is the total density, has a minimum, with an equilibrium density that can be adjusted by the distance $d$ between the layers (decreasing with increasing $d$). The attraction necessary for a self-bound liquid comes from the interlayer dipole-dipole interaction that leads to a mediated intralayer attraction. We investigate the regime of negative pressure towards the spinodal instability, where the bilayer is unstable against infinitesimal fluctuations of the total density, confirmed by calculations of the speed of sound of total density fluctuations.

We introduce an approach for fine grading of plasmonic ellipsoidal nanoparticles by two interfering light beams. We consider electrically neutral subwavelength metal nanoparticles whose response is described within the dipole approximation. For the ellipsoidal nanoparticles, we find that their polarizability tensor is strongly dispersive due to the existence of two orthogonal plasmon modes. These modes can be resonantly excited by light and the optical force experienced by particles depends on the ratio of ellipsoid semiaxes. This dependence allows us to spatially separate ellipsoidal particles with different aspect ratio. The eigenfrequencies of plasmons depend on the depolarization factor as well as on the permittivity of the environment and therefore our results can potentially be employed in a wide frequency range including near infrared, visible, and ultraviolet.

The contribution of two types of cascading process to the nonlinear optical diffraction of electromagnetic waves from a standing acoustic wave in a GaAs crystal is theoretically studied. The first type of cascading process results from second-harmonic generation followed by linear acousto-optical diffraction, while the second type involves linear acousto-optical diffraction from the standing acoustic wave and subsequent sum-frequency generation. In contrast to the third, direct, nonlinear acousto-optical diffraction process we previously investigated, the photoelastic interaction between electromagnetic and acoustic waves is here linear. We establish the rules governing the cascading processes and show that in most cases the output signal simultaneously results from two or even three of the possible nonlinear diffraction mechanisms. However, we demonstrate that a careful choice of the incidence angles of the incoming electromagnetic waves, of the polarization combinations of the incoming and diffracted waves, and of the type of acoustic wave (longitudinal or transverse) makes it always possible to distinguish between the direct and either of the two cascading processes.

Witnessing continuous-variable Bell nonlocality is a challenging endeavor, but Bell himself showed how one might demonstrate this nonlocality. Although Bell nearly showed a violation using the Clauser-Horne-Shimony-Holt (CHSH) inequality with sign-binned position-momentum statistics of entangled pairs of particles measured at different times, his demonstration is subject to approximations not realizable in a laboratory setting. Moreover, he does not give a quantitative estimation of the maximum achievable violation for the wave function he considers. In this article, we show how his strategy can be reimagined using the transverse positions and momenta of entangled photon pairs measured at different propagation distances, and we find that the maximum achievable violation for the state he considers is actually very small relative to the upper limit of $2\sqrt{2}$. Although Bell's wave function does not produce a large violation of the CHSH inequality, other states may yet do so.

We establish a generic method to analyze the time evolution of open quantum many-body systems. Our approach is based on a variational integration of the quantum master equation describing the dynamics and naturally connects to a variational principle for its nonequilibrium steady state. We successfully apply our variational method to study dissipative Rydberg gases, finding very good quantitative agreement with small-scale simulations of the full quantum master equation. We observe that correlations related to non-Markovian behavior play a significant role during the relaxation dynamics towards the steady state. We further quantify this non-Markovianity and find it to be closely connected to an information-theoretical measure of quantum and classical correlations.

Einstein-Smoluchowski diffusion, damped harmonic oscillations, and spatial decoherence are special cases of an elegant class of Markovian quantum Brownian motion models that is invariant under linear symplectic transformations. Here we prove that for each member of this class there is a preferred timescale such that the dynamics, considered stroboscopically, can be re-written exactly as unitary evolution interrupted periodically by an entanglement-breaking measurement with respect to a fixed overcomplete set of pure Gaussian states. This is relevant to the continuing search for the best way to describe pointer states and pure decoherence in systems with continuous variables, and gives a concrete sense in which the decoherence can be said to arise from a complete measurement of the system by its environment. We also extend some of the results of Diósi and Kiefer to the symplectic covariant formalism and compare them with the preferred time scales and Gaussian states associated with the POVM form.

Gottesman, Kitaev, and Preskill have formulated a way of encoding a qubit into an oscillator such that the qubit is protected against small shifts (translations) in phase space. The idea underlying this encoding is that error processes of low rate can be expanded into small shift errors. The qubit space is defined as an eigenspace of two mutually commuting displacement operators $S_p$ and $S_q$ which act as large shifts or translations in phase space. We propose and analyze the approximate creation of these qubit states by coupling the oscillator to a sequence of ancilla qubits. This preparation of the states uses the idea of phase estimation where the phase of the displacement operator, say $S_p$, is approximately determined. We consider several possible forms of phase estimation. We analyze the performance of repeated and adaptive phase estimation as the simplest and experimentally most viable schemes given a realistic upper limit on the number of photons in the oscillator. We propose a detailed physical implementation of this protocol using the dispersive coupling between a transmon ancilla qubit and a cavity mode in circuit QED. We provide an estimate that in a current experimental setup one can prepare a good code state from a squeezed vacuum state using eight rounds of adaptive phase estimation, lasting in total about $4\mu \text{s}$, with $94\%$ (heralded) chance of success.

In the dispersive regime of qubit-cavity coupling, a classical cavity drive populates the cavity but leaves the qubit state unaffected. However, the dispersive Hamiltonian is derived after both a frame transformation and an approximation. Therefore, to connect to external experimental devices, the inverse frame transformation from the dispersive frame back to the laboratory frame is necessary. In this work we show that in the laboratory frame the system is best described by an entangled state known as the dressed coherent state, and thus even in the dispersive regime, entanglement is generated between the qubit and the cavity. Also, we show that further qubit evolution depends on both the amplitude and phase of the dressed coherent state and use the dressed coherent state to calculate the measurement contrast of a recently developed dispersive readout protocol.