We discuss the topological $p_x+{\mathit{ip}}_y$ superfluid phase in a two-dimensional (2D) gas of single-component fermionic polar molecules dressed by a circularly polarized microwave field. This phase emerges because the molecules may interact with each other via a potential $V_0(r)$ that has an attractive dipole-dipole $1/r^3$ tail, which provides $p$-wave superfluid pairing at fairly high temperatures. We calculate the amplitude of elastic $p$-wave scattering in the potential $V_0(r)$ taking into account both the anomalous scattering due to the dipole-dipole tail and the short-range contribution. This amplitude is then used for the analytical and numerical solution of the renormalized BCS gap equation which includes the second-order Gor’kov-Melik-Barkhudarov corrections and the correction related to the effective mass of the quasiparticles. We find that the critical temperature $T_c$ can be varied within a few orders of magnitude by modifying the short-range part of the potential $V_0(r)$. The decay of the system via collisional relaxation of molecules to dressed states with lower energies is rather slow due to the necessity of a large momentum transfer. The presence of a constant transverse electric field reduces the inelastic rate, and the lifetime of the system can be of the order of seconds even at 2D densities $~{10}^9$ cm${}^{-2}$. This leads to $T_c$ of up to a few tens of nanokelvins and makes it realistic to obtain the topological $p_x+{\mathit{ip}}_y$ phase in experiments with ultracold polar molecules.

A path-integral approach to the quantization of the electromagnetic field in a linearly amplifying magnetodielectric medium is presented. Two continua of inverted harmonic oscillators are used to describe the polarizability and magnetizability of the amplifying medium. The causal susceptibilities of the amplifying medium, with negative imaginary parts in finite frequency intervals, are identified and their relationships to microscopic coupling functions are determined. By carefully relating the two-point functions of the field theory to the optical Green functions, we calculate the Casimir energy and Casimir forces for a multilayer magnetodielectric medium with both gain and loss. We point out the essential differences with a purely passive layered medium. For a single layer, we find different bounds on the Casimir force for fully amplifying and for lossy media. The force is attractive in both cases, even if the medium exhibits negative refraction. From our Lagrangian we also derive by canonical quantization the postulates of the phenomenological theory of amplifying magnetodielectrics.

We present here the results of our relativistic many-body calculations of various properties of the first six low-lying excited states of indium. The calculations were performed using the relativistic coupled-cluster method in the framework of the singles, doubles, and partial triples approximation. The lifetime of the $[4p^6]5s^{2}5p_{3/2}$ state in this atom is determined. Our results could be used to shed light on the reliability of the lifetime measurements of the excited states of atomic indium that we have considered in the present work.

A enhanced procedure implementing the finite-element-discrete-model method [R. K. Nesbet, Phys. Rev. A 24,1184 (1981)] for determining atomic or molecular shape resonances and widths is described. The present procedure includes an approximation for the static exchange plus polarization model involving Möller-Plesset perturbation theory. Applications to Mg, ${\mathrm{N}}_2$, CH${}_2$O, and uracil are described. Compared with experiment, the results for Mg are within $5$ meV for the resonance position and $75$ meV for the width. The vertical geometry results for ${\mathrm{N}}_2$ and CH${}_2$O compare well with experiment insofar as can be determined in the presence of nuclear motion complications. Uracil is calculated as an example where the large dipole moment ($4.8$ D) has an impact on threshold properties and possible dipole bound states.

The influence upon molecular photoionization dynamics of vibrational motion of the nuclei in both the initial (neutral) state and the final (molecular ion) state is examined using a consistent theoretical treatment applied to the wide range of existing experimental data for the benchmark CO C $1s^{-1}$ $K$-shell ionization. This allows comparisons to be made against cross sections, lab-frame $\beta$-parameter measurements, and molecule-frame photoelectron angular distributions that have all been recorded both with, and without, ion vibrational-state resolution. A relatively simple multiple-scattering treatment works well in all these applications, its performance comparing very favorably with alternative relaxed core Hartree-Fock methods. The calculations are extended to examine possible effects of vibrational excitation in the neutral, and show marked effects that extend to energies lying away from the obvious center of the CO σ${}^{*}$ shape resonance.

We show that the generators of quantum states of light can be built by employing the Kerr nonlinearity, a strong linear absorption or losses, and the linear coupling of optical modes. Our setup can be realized, for instance, with the use of the optical fiber technology. We consider in detail the simplest cases of three and four coupled modes, where a strongly lossy mode is linearly coupled to other linear and nonlinear modes. In the three-mode design, our scheme emulates the third-order nonlinear absorption, allowing for generation of the single-photon states, or two-photon absorption allowing the generation of the phase states. In the four-mode design, the scheme emulates a nonlocal absorption which produces an entangled state of two uncoupled modes. We also note that in the latter case and in the case of phase state generation the output state is in the linear mode, which prevents its subsequent degradation by strong losses accompanying a strong Kerr nonlinearity.

Entangled states can potentially be used to outperform the standard quantum limit by which every classical sensor is bounded. However, entangled states are very susceptible to decoherence, and so it is not clear whether one can really create a superior sensor to classical technology via a quantum strategy which is subject to the effect of realistic noise. This paper presents an investigation of how a quantum sensor composed of many spins is affected by independent dephasing. We adopt general noise models including non-Markovian effects, and in these noise models the performance of the sensor depends crucially on the exposure time of the sensor to the field. We have found that, by choosing an appropriate exposure time within the non-Markovian time region, an entangled sensor does actually beat the standard quantum limit. Since independent dephasing is one of the most typical sources of noise in many systems, our results suggest a practical and scalable approach to beating the standard quantum limit.

We study the spin-orbital interaction and the spin Hall effect of an electron moving on a noncommutative space under the influence of a vector potential $\mathrm{A⃗}$. On a noncommutative space, we find that the commutator between the vector potential $\mathrm{A⃗}$ and the electric potential $V_1(\mathrm{r⃗})$ of the lattice induces a new term, which can be treated as an effective electric field, and the spin Hall conductivity obtains some correction. On a noncommutative space, the spin current and spin Hall conductivity have distinct values in different directions, and depend explicitly on the noncommutative parameter. Once this spin Hall conductivity in different directions can be measured experimentally with a high level of accuracy, the data can then be used to impose bounds on the value of the space noncommutativity parameter. We have also defined a new parameter, $\varsigma =\rho \theta$ ($\rho$ is the electron concentration, $\theta$ is the noncommutativity parameter), which can be measured experimentally. Our approach is based on the Foldy-Wouthuysen transformation, which gives a general Hamiltonian of a nonrelativistic electron moving on a noncommutative space.

We investigate how the entanglement properties of a two-mode state can be improved by performing a coherent superposition operation $t\mathrm{â}+r{\mathrm{â}}^{†}$ of photon subtraction and addition, proposed by Lee and Nha [Phys. Rev. A 82, 053812 (2010)], on each mode. We show that the degree of entanglement, the Einstein-Podolsky-Rosen–type correlation, and the performance of quantum teleportation can be all enhanced for the output state when the coherent operation is applied to a two-mode squeezed state. The effects of the coherent operation are more prominent than those of the mere photon subtraction $\mathrm{â}$ and the addition ${\mathrm{â}}^{†}$ particularly in the small-squeezing regime, whereas the optimal operation becomes the photon subtraction (case of $r=0$) in the large-squeezing regime.

We show that, for a finite-dimensional Hilbert space, there exist observables that induce a tensor product structure such that the entanglement properties of any pure state can be tailored. In particular, we provide an explicit, finite method for constructing observables in an unstructured $d$-dimensional system so that an arbitrary known pure state has any Schmidt decomposition with respect to an induced bipartite tensor product structure. In effect, this article demonstrates that, in a finite-dimensional Hilbert space, entanglement properties can always be shifted from the state to the observables and all pure states are equivalent as entanglement resources in the ideal case of complete control of observables.

A subspace of a multipartite Hilbert space is said to be locally indistinguishable if any orthonormal basis of this subspace cannot be perfectly distinguished by local operations and classical communication. Previously it was shown that any $m\otimes n$ bipartite system with $m>2$ and $n>2$ has a locally indistinguishable subspace. However, it has been an open problem since 2005 whether there is a locally indistinguishable bipartite subspace with a qubit subsystem. We settle this problem in negative by showing that any $2\otimes n$ bipartite subspace contains a basis that is locally distinguishable. As an interesting application, we show that any quantum channel with two Kraus operators has optimal environment-assisted classical capacity.

We study how dynamical decoupling (DD) pulse sequences can improve the reliability of quantum computers. We prove upper bounds on the accuracy of DD-protected quantum gates and derive sufficient conditions for DD-protected gates to outperform unprotected gates. Under suitable conditions, fault-tolerant quantum circuits constructed from DD-protected gates can tolerate stronger noise and have a lower overhead cost than fault-tolerant circuits constructed from unprotected gates. Our accuracy estimates depend on the dynamics of the bath that couples to the quantum computer and can be expressed either in terms of the operator norm of the bath’s Hamiltonian or in terms of the power spectrum of bath correlations; we explain in particular how the performance of recursively generated concatenated pulse sequences can be analyzed from either viewpoint. Our results apply to Hamiltonian noise models with limited spatial correlations.

We consider the smallest possible directional reference frames allowed and determine the best one can ever do in preserving quantum information in various scenarios. We find that for the preservation of a single spin state, two orthogonal spins are optimal primitive reference frames; and in a product state, they do approximately $22\%$ as well as an infinite-sized classical frame. By adding a small amount of entanglement to the reference frame, this can be raised to $2(2/3){}^5=26\%$. Under the different criterion of entanglement preservation, a very similar optimal reference frame is found; however, this time it is for spins aligned at an optimal angle of ${87}^{°}$. In this case $24\%$ of the negativity is preserved. The classical limit is considered numerically, and indicates under the criterion of entanglement preservation, that ${90}^{°}$ is selected out nonmonotonically, with a peak optimal angle of ${96.5}^{°}$ for $L=3$ spins.

We study the energetics and dispersion of anomalous dimers that are induced by the Pauli blocking effect in a quantum Fermi gas of majority atoms near interspecies resonances. Unlike in vacuum, we find that both the sign and magnitude of the dimer masses are tunable via Feshbach resonances. We also investigate the effects of particle-hole fluctuations on the dispersion of dimers and demonstrate that the particle-hole fluctuations near a Fermi surface (with Fermi momentum $\hslash k_F$) generally reduce the effective two-body interactions and the binding energy of dimers. Furthermore, in the limit of light minority atoms the particle-hole fluctuations disfavor the formation of dimers with a total momentum $\hslash k_F$, because near $\hslash k_F$ the modes where the dominating particle-hole fluctuations appear are the softest. Our calculation suggests that near broad interspecies resonances when the minority-majority mass ratio $m_B/m_F$ is smaller than a critical value (estimated to be $0.136$), dimers in a finite-momentum channel are energetically favored over dimers in the zero-momentum channel. We apply our theory to quantum gases of ${}^6\mathrm{Li}$${}^{40}\mathrm{K}$, ${}^6\mathrm{Li}$${}^{87}\mathrm{Rb}$, ${}^{40}\mathrm{K}$${}^{87}\mathrm{Rb}$, and ${}^6\mathrm{Li}$${}^{23}\mathrm{Na}$ near broad interspecies resonances, and discuss the limitations of our calculations and implications.

The effective Hamiltonian describing resonant interaction of an ensemble of identical quantum particles with a photon-free vacuum electromagnetic field has been obtained with allowance for terms of second order in the coupling constant (the Stark interaction) by means of the perturbation theory on the basis of the unitary transformation of the system quantum state. It has been shown that in the Markov approximation the effective Hamiltonian terms of first order in the coupling constant are represented by the quantum Wiener process, whereas terms of second order are expressed by the quantum Poisson process. During the course of the investigation, it was established that the Stark interaction played a significant role in the ensemble dynamics, thus influencing the collective spontaneous decay of the ensemble of an appreciably high number of identical particles. Fundamental effects have been discovered, i.e., the excitation conservation in a sufficiently dense ensemble of identical particles and superradiance suppression in the collective decaying process of an excited ensemble with a determined number of particles.

Fractional time derivative, an abstract mathematical operator of fractional calculus, is used to describe the real optical system of a V-type three-level atom embedded in a photonic crystal. A fractional kinetic equation governing the dynamics of the spontaneous emission from this optical system is obtained as a fractional Langevin equation. Solving this fractional kinetic equation by fractional calculus leads to the analytical solutions expressed in terms of fractional exponential functions. The accuracy of the obtained solutions is verified through reducing the system into the special cases whose results are consistent with the experimental observation. With accurate physical results and avoiding the complex integration for solving this optical system, we propose fractional calculus with fractional time derivative as a better mathematical method to study spontaneous emission dynamics from the optical system with non-Markovian dynamics.

This research focuses on a coherently driven four-level atomic medium with the aim of inducing a negative index of refraction while taking into consideration local field corrections as well as magnetoelectric cross coupling (i.e.,chirality) within the material’s response functions. Two control fields are used to render the medium transparent for a probe field which simultaneously couples to an electric and a magnetic dipole transition, thus allowing one to test the permittivity and permeability of the material at the same time. Numerical simulations show that a negative index of refraction with low absorption can be obtained for a range of probe detunings while depending on number density and the ratio between the intensities of the control fields.

The enhancement and suppression of the two coexisting six-wave mixing (SWM) processes via atomic coherence have been observed. In the presence of mutual dressing between two SWM signals, the self-dressing effect causes the Autler-Townes (AT) splitting of the SWM signals and the external-dressing effect makes the SWM signals enhanced or suppressed. In addition, the power dependencies of the enhancement and suppression of SWM processes are studied. Theoretical calculations are carried out, which are in good agreement with the experimental results.

A multiparty protocol for distributed quantum clock synchronization has been claimed to provide universal limits on the clock accuracy, viz., that accuracy monotonically decreases with the number $n$ of party members. But this is only true for synchronization when one limits oneself to $W$ states. This work shows that the usage of Z (Symmetric Dicke) states, a generalization of $W$ states, results in improved accuracy, having a maximum when $\lfloor n/2\rfloor$ of its members have their qubits with a $|1\rangle$ eigenstate.

We theoretically study the light propagation at the zigzag edges of a honeycomb photonic crystal (PC), or photonic graphene. It is found that the corresponding edge states have a sinusoidal dispersion similar to those found in PC coupled resonator optical waveguides [CROWs; M. Notomi et al., Nature Photon. 2, 741 (2008)]. The sinusoidal dispersion curve can be made very flat by carefully tuning edge parameters. As a result, low group velocity and small group velocity dispersion can be simultaneously obtained for light propagating at the zigzag edge of photonic graphene. Compared with PC CROWs, our slow-light system exhibits no intrinsic radiation loss and has a larger group velocity bandwidth product. Our results could find applications in on-chip optical buffers and enhanced light-matter interaction.