An arbitrary initial state of an optical or microwave field in a lossy driven nonlinear cavity can be changed into a partially incoherent superposition of only the vacuum and the single-photon states. This effect is known as single-photon blockade, which is usually analyzed for a Kerr-type nonlinear cavity parametrically driven by a single-photon process assuming single-photon loss mechanisms. We study photon blockade engineering via a nonlinear reservoir, i.e., a quantum reservoir, where only two-photon absorption is allowed. Namely, we analyze a lossy nonlinear cavity parametrically driven by a two-photon process and allowing two-photon loss mechanisms, as described by the master equation derived for a two-photon absorbing reservoir. The nonlinear cavity engineering can be realized by a linear cavity with a tunable two-level system via the Jaynes-Cummings interaction in the dispersive limit. We show that by tuning properly the frequencies of the driving field and the two-level system, the steady state of the cavity field can be the single-photon Fock state or a partially incoherent superposition of several Fock states with photon numbers, e.g., (0,2), (1,3), (0,1,2), or (0,2,4). At the right (now fixed) frequencies, we observe that an arbitrary initial coherent or incoherent superposition of Fock states with an even (odd) number of photons is changed into a partially incoherent superposition of a few Fock states of the same photon-number parity. We find analytically approximate formulas for these two kinds of solutions for several differently tuned systems. A general solution for an arbitrary initial state is a weighted mixture of the above two solutions with even and odd photon numbers, where the weights are given by the probabilities of measuring the even and odd numbers of photons of the initial cavity field, respectively. This can be interpreted as two separate evolution-dissipation channels for even and odd-number states. Thus, in contrast to the standard predictions of photon blockade, we prove that the steady state of the cavity field, in the engineered photon blockade, can depend on its initial state. To make our results more explicit, we analyze photon blockades for some initial infinite-dimensional quantum and classical states via the Wigner and photon-number distributions.

We study the photon-photon correlation properties of two-photon transport in a one-dimensional waveguide coupled to a nonlinear cavity via a real-space approach. It is shown that the intrinsic dissipation of the nonlinear cavity has an important effect upon the correlation of the transported photons. More importantly, strongly correlated photons can be obtained in the transmitted photons even when the nonlinear interaction strength is weak in the cavity. The strong photon-photon correlation is induced by the Fano resonance involving destructive interference between the plane wave and bound state for two-photon transport.

Identifying weakly coupled nuclear spins around single electron spins is a key step toward implementing quantum information processing using coupled electron-nuclei spin systems or sensing like single-spin nuclear magnetic resonance detection using diamond defect spins. Dynamical decoupling control of the center electron spin with periodic pulse sequences [e.g., the Carre-Purcell-Meiboom-Gill (CPMG) sequence] has been successfully used to identify single nuclear spins and to resolve structure of nuclear spin clusters. Here, we design a type of pulse sequence by replacing the repetition unit (a single $\pi$ pulse) of the CPMG sequence with a group of nonuniformly spaced $\pi$ pulses. Using the nitrogen-vacancy center system in diamond, we theoretically demonstrate that the designed pulse sequence improves the resolution of nuclear spin noise spectroscopy, and more information about the surrounding nuclear spins is extracted. The principle of dynamical decoupling design proposed in this paper is useful in many systems (e.g., defect spin qubit in solids, trapped ion, and superconducting qubit) for high-resolution noise spectroscopy.

Phase-randomized light is one of the key assumptions in the security proof of the Bennett-Brassard 1984 (BB84) quantum-key-distribution (QKD) protocol using an attenuated laser. Though the assumption has been believed to be satisfied for conventional systems, it should be reexamined for current high-speed QKD systems. The phase correlation may be induced by the overlap of the optical pulses, the interval of which decreases as the clock frequency increases. The phase randomness was investigated experimentally by measuring the visibility of interference. An asymmetric Mach-Zehnder interferometer was used to observe the interference between adjacent pulses from a gain-switched distributed feedback laser diode driven at 10 GHz. Low visibility was observed when the minimum drive current was set far below the threshold, while interference emerged when the minimum drive current was close to the threshold. The theoretical evaluation on the impact of the imperfect phase randomization provides target values for the visibility to guarantee the phase randomness. The experimental and theoretical results show that secure implementation of decoy BB84 protocol is achievable even for the 10-GHz clock frequency by using the laser diode under proper operating conditions.

The radiative association processes for ${\mathrm{Na}}^{+}$ colliding with ${}^{87}\mathrm{Rb}\left(5s\right)$ atoms have been investigated by using the quantum-mechanical method. The total and partial cross sections that associate to the specific rovibrational states are calculated rigorously in the energy range of ${10}^{-13}-1.2\times {10}^{-2}\mathrm{eV}$. The association cross sections display rich resonance structures. The ratios of rotationally resolved cross sections to total association cross sections and the ratios of vibrationally resolved cross sections to rotationally resolved cross sections are calculated and presented. For energies less than ${10}^{-9}\mathrm{eV}$, association to $X{}^2{\Sigma }^{+}$ ($J=1$) dominates over all other association states. As the energy increases, each resonance of the total cross sections is associated with the given angular component of specific bound states. In the energy range of ${10}^{-13}-1.2\times {10}^{-3}\mathrm{eV}$, the vibrational states $v=27$ and $v=28$ are the most probable final states. The probability for the formation of molecular ion ${\mathrm{NaRb}}^{+}$ in the rovibrational states is discussed. The existence of Cooper minima in the radiative association cross sections is found and illustrated.

We propose a theoretical scheme for realizing selective coherent spin transportation in a spin-orbit-coupled bosonic gas trapped in a symmetric double well by fast modulation of the energy-level unbalance between the two wells. The modulation can be tuned in such a way that an arbitrarily, a priori prescribed spin type (single spin or a spin pair with opposite spins) and the number of these spin bosons with or without spin flipping are allowed to tunnel. Furthermore, prescribed superexchange of spin bosons (where only pure spin exchange is allowed between the two wells and the atom number in each well is not changed) is also presented. The resonance conditions of realizing this selective coherent spin transportation are obtained analytically and confirmed numerically. This engineering provides a possible means for spin control and accurate counting or efficient filtering of the number of spins.

We study in three dimensions the problem of a spatially homogeneous zero-temperature ideal Fermi gas of spin-polarized particles of mass $m$ perturbed by the presence of a single distinguishable impurity of mass $M$. The interaction between the impurity and the fermions involves only the partial $s$ wave through the scattering length $a$ and has negligible range $b$ compared to the inverse Fermi wave number $1/k_{\mathrm{F}}$ of the gas. Through the interactions with the Fermi gas the impurity gives birth to a quasiparticle, which will be here a Fermi polaron (or more precisely a monomeron). We consider the general case of an impurity moving with wave vector $\mathbf{K}\ne \mathbf{0}$: Then the quasiparticle acquires a finite lifetime in its initial momentum channel because it can radiate particle-hole pairs in the Fermi sea. A description of the system using a variational approach, based on a finite number of particle-hole excitations of the Fermi sea, then becomes inappropriate around $\mathbf{K}=\mathbf{0}$. We rely thus upon perturbation theory, where the small and negative parameter $k_{\mathrm{F}}a\to 0^{-}$ excludes any branches other than the monomeronic one in the ground state (as, e.g., the dimeronic one), and allows us a systematic study of the system. We calculate the impurity self-energy ${\Sigma }^{\left(2\right)}(\mathbf{K},\omega )$ up to second order included in $a$. Remarkably, we obtain an analytical explicit expression for ${\Sigma }^{\left(2\right)}(\mathbf{K},\omega )$, allowing us to study its derivatives in the plane $(K,\omega )$. These present interesting singularities, which in general appear in the third-order derivatives ${\partial }^3{\Sigma }^{\left(2\right)}(\mathbf{K},\omega )$. In the special case of equal masses, $M=m$, singularities appear already in the physically more accessible second-order derivatives ${\partial }^2{\Sigma }^{\left(2\right)}(\mathbf{K},\omega )$; using a self-consistent heuristic approach based on ${\Sigma }^{\left(2\right)}$ we then regularize the divergence of the second-order derivative ${\partial }_K^2\Delta E\left(\mathbf{K}\right)$ of the complex energy of the quasiparticle found in Trefzger and Castin [Europhys. Lett. 104, 50005 (2013)] at $K=k_{\mathrm{F}}$, and we predict an interesting scaling law in the neighborhood of $K=k_{\mathrm{F}}$. As a by product of our theory we have access to all moments of the momentum of the particle-hole pair emitted by the impurity while damping its motion in the Fermi sea at the level of Fermi's golden rule.

We demonstrate tomographic reconstruction of the phase space distribution of atoms oscillating in a harmonic trap with weak potential corrugation caused by nanoscale imperfections in an atom chip. We find that deformations in these distributions are highly sensitive to anharmonic components of the potential. They are explained in terms of angular velocity dispersion of isoenergetic phase space trajectories. We show that the method is applicable for probing classical and quantum dynamics of cold atoms, and we note its importance for future technological applications.

In the uncertainty budget of primary atomic cesium fountain clocks, evaluations of frequency-pulling shifts of the hyperfine clock transition caused by unintentional excitation of its nearby transitions (Rabi and Ramsey pulling) have been based so far on an approach developed for cesium beam clocks. We re-evaluate this type of frequency pulling in fountain clocks and pay particular attention to the effect of initial coherent atomic states. We find significantly enhanced frequency shifts caused by Ramsey pulling due to sublevel population imbalance and corresponding coherences within the state-selected hyperfine component of the initial atom ground state. Such shifts are experimentally investigated in an atomic fountain clock and quantitative agreement with the predictions of the model is demonstrated.

We investigate the parity- and time-reversal ($\mathcal{PT}$-) symmetry breaking in lattice models in the presence of long-ranged, non-Hermitian, $\mathcal{PT}$-symmetric potentials that remain finite or become divergent in the continuum limit. By scaling analysis of the fragile $\mathcal{PT}$ threshold for an open finite lattice, we show that continuum loss-gain potentials $V_{\alpha }\left(x\right)\propto i{\left|x\right|}^{\alpha }\mathrm{sgn}\left(x\right)$ have a positive $\mathcal{PT}$-breaking threshold for $\alpha >-2$, and a zero threshold for $\alpha \le -2$. When $\alpha <0$ localized states with complex (conjugate) energies in the continuum energy band occur at higher loss-gain strengths. We investigate the signatures of $\mathcal{PT}$-symmetry breaking in coupled waveguides, and show that the emergence of localized states dramatically shortens the relevant time scale in the $\mathcal{PT}$-symmetry broken region.

We consider an analytical approach that involves the complex poles of the propagator to investigate the effect due to the lack of time-reversal invariance on the time evolution of decay for purely absorptive potentials. We find that the choice of the initial state may change the exponential decaying regime into a nonexponential oscillatory behavior at time scales of the order of a lifetime of the system. We illustrate this effect for a spectral singularity corresponding to a purely imaginary $\delta$-shell potential.

For qubits, Monte Carlo estimation of the average fidelity of Clifford unitaries is efficient: it requires a number of experiments that is independent of the number $n$ of qubits and classical computational resources that scale only polynomially in $n$. Here, we identify the requirements for efficient Monte Carlo estimation and the corresponding properties of the measurement operator basis when replacing two-level qubits by $p$-level qudits. Our analysis illuminates the intimate connection between mutually unbiased measurements and the existence of unitaries that can be characterized efficiently. It allows us to propose a “hierarchy” of generalizations of the standard Pauli basis from qubits to qudits according to the associated scaling of resources required in Monte Carlo estimation of the average fidelity.

A bipartite state ${\rho }_{AB}$ is symmetric extendible if there exists a tripartite state ${\rho }_{AB{B}^{\prime }}$ whose $AB$ and $A{B}^{\prime }$ marginal states are both identical to ${\rho }_{AB}$. Symmetric extendibility of bipartite states is of vital importance in quantum information because of its central role in separability tests, one-way distillation of Einstein-Podolsky-Rosen pairs, one-way distillation of secure keys, quantum marginal problems, and antidegradable quantum channels. We establish a simple analytic characterization for symmetric extendibility of any two-qubit quantum state ${\rho }_{AB}$; specifically, $\mathrm{tr}\left({\rho }_B^2\right)\ge \mathrm{tr}\left({\rho }_{AB}^2\right)-4\sqrt{det{\rho }_{AB}}$. As a special case we solve the bosonic three-representability problem for the two-body reduced density matrix.

Cryogenic buffer-gas beams are a promising method for producing bright sources of cold molecular radicals for cold-collision and chemical-reaction experiments. In order to use these beams in studies of reactions with controlled collision energies or in trapping experiments, one needs a method of controlling the forward velocity of the beam. A Stark decelerator can be an effective tool for controlling the mean speed of molecules produced by supersonic jets, but efficient deceleration of buffer-gas beams presents new challenges due to longer pulse lengths. Traveling-wave decelerators are uniquely suited to meet these challenges because of their ability to confine molecules in three dimensions during deceleration and their versatility afforded by the analog control of the electrodes. We have created ground-state $\mathrm{CH}\left(X{}^2\Pi \right)$ radicals in a cryogenic buffer-gas cell with the potential to produce a cold molecular beam of ${10}^{11}$ molecules/pulse. We present a general protocol for Stark deceleration of beams with a large position and velocity spread for use with a traveling-wave decelerator. Our method involves confining molecules transversely with a hexapole for an optimized distance before deceleration. This rotates the phase-space distribution of the molecular packet so that the packet is matched to the time-varying phase-space acceptance of the decelerator. We demonstrate with simulations and an analytic one-dimensional model that this method can decelerate a significant fraction of the molecules in successive wells of a traveling-wave decelerator to produce energy-tuned beams for cold and controlled-molecule experiments.

Recently, violation of the Cauchy-Schwarz inequality by the second-order correlation function was reported in a collection of ultracold bosons [Kheruntsyan et al., Phys. Rev. Lett. 108, 260401 (2012)]. We show that the observation of this effect proves the presence of particle entanglement in a many-body system of bosons. Our derivation is based on the analogy between the coherent states of electromagnetic fields and separable states of massive particles. The presented argument applies to any quantum system of identical bosons with either a fixed or a fluctuating number of particles, provided that there is no coherence between different number states.

We present a general scheme to realize a cold-atom quantum simulator of bidimensional atomic crystals. Our model is based on the use of two independently trapped atomic species: the first one, subject to a strong in-plane confinement, constitutes a two-dimensional matter wave which interacts only with atoms of the second species, deeply trapped around the nodes of a two-dimensional optical lattice. By introducing a general analytic approach we show that the system Green function can be exactly determined, allowing for the investigation of the matter-wave transport properties. We propose some illustrative applications to both Bravais (square, triangular) and non-Bravais (graphene, kagomé) lattices, studying both ideal periodic systems and experimental-size and disordered ones. Some remarkable spectral properties of these atomic artificial lattices are pointed out, such as the emergence of single and multiple gaps, flat bands, and Dirac cones. All these features can be manipulated via the interspecies interaction, which proves to be widely tunable due to the interplay between scattering length and confinements.

The balances of the electromagnetic powers and momentum flows for the system of a dielectric particle and a dielectric slab waveguide are studied. The emphasis is made on the regime when whispering gallery resonances in the particle are excited. The excitation is achieved by a guided mode that has either transverse electric or magnetic polarization. The scattering problem is solved by using an analytical representation of the solution with subsequent numerical approach to find the scattered fields with high accuracy. It accounts rigorously for the interaction between the particle and the waveguide. It is found that the propelling force on the particle can be comparable to or even exceed the value of the momentum flow of the incident mode. This is related to a highly anisotropic angular distribution of the bulk radiation that can carry some noticeable momentum in the longitudinal direction. The bulk radiation carries also nonvanishing momentum in the transverse direction giving rise to a difference in the transverse forces experienced by the particle and by the waveguide. The strong coupling between the particle and the waveguide operating in the single-mode regime is shown to upshift slightly the resonant frequencies with decreasing gap between the particle and the waveguide.

High spectral mode density of conventional optical cavities is detrimental to the generation of broad optical frequency combs and to other linear and nonlinear applications. In this work we optimize the morphology of high-$Q$ whispering gallery (WG) and Fabry-Perot (FP) cavities and find a set of parameters that allows treating them, essentially, as single-mode structures, thus removing limitations associated with a high density of cavity mode spectra. We show that both single-mode WGs and single-mode FP cavities have similar physical properties, in spite of their different loss mechanisms. The morphology optimization does not lead to a reduction of quality factors of modes belonging to the basic family. We study the parameter space numerically and find the region where the highest possible $Q$ factor of the cavity modes can be realized while just having a single bound state in the cavity. The value of the $Q$ factor is comparable with that achieved in conventional cavities. The proposed cavity structures will be beneficial for generation of octave spanning coherent frequency combs and will prevent undesirable effects of parametric instability in laser gravitational wave detectors.

We investigate theoretically the formation of two-component light with superluminal group velocity in a medium controlled by four Raman pump fields. In such an optical scheme only a particular combination of the probe fields is coupled to the matter and exhibits superluminal propagation; the orthogonal combination is uncoupled. The individual probe fields do not have a definite group velocity in the medium. Calculations demonstrate that this superluminal component experiences an envelope advancement in the medium with respect to the propagation in vacuum.