The Salecker-Wigner-Peres (SWP) clock is often used to determine the duration a quantum particle is supposed to spend in a specified region of space $\mathrm{\Omega }$. By construction, the result is a real positive number, and the method seems to avoid the difficulty of introducing complex time parameters, which arises in the Feynman paths approach. However, it tells little about the particle's motion. We investigate this matter further, and show that the SWP clock, like any other Larmor clock, correlates the rotation of its angular momentum with the durations $\tau$, which the Feynman paths spend in $\mathrm{\Omega }$, thereby destroying interference between different durations. An inaccurate weakly coupled clock leaves the interference almost intact, and the need to resolve the resulting “which way?” problem is one of the main difficulties at the center of the “tunnelling time” controversy. In the absence of a probability distribution for the values of $\tau$, the SWP results are expressed in terms of moduli of the “complex times,” given by the weighted sums of the corresponding probability amplitudes. It is shown that overinterpretation of these results, by treating the SWP times as physical time intervals, leads to paradoxes and should be avoided. We also analyze various settings of the SWP clock, different calibration procedures, and the relation between the SWP results and the quantum dwell time. The cases of stationary tunneling and tunnel ionization are considered in some detail. Although our detailed analysis addresses only one particular definition of the duration of a tunneling process, it also points towards the impossibility of uniting various time parameters, which may occur in quantum theory, within the concept of a single tunnelling time.

The state of a continuously monitored qubit evolves stochastically, exhibiting competition between coherent Hamiltonian dynamics and diffusive partial collapse dynamics that follow the measurement record. We couple these distinct types of dynamics together by linearly feeding the collected record for dispersive energy measurements directly back into a coherent Rabi drive amplitude. Such feedback turns the competition cooperative and effectively stabilizes the qubit state near a target state. We derive the conditions for obtaining such dispersive state stabilization and verify the stabilization conditions numerically. We include common experimental nonidealities, such as energy decay, environmental dephasing, detector efficiency, and feedback delay, and show that the feedback delay has the most significant negative effect on the feedback protocol. Setting the measurement collapse time scale to be long compared to the feedback delay yields the best stabilization.

We consider the problem of minimum-error quantum state discrimination for single-qubit mixed states. We present a method which uses the Helstrom conditions constructively and analytically; this algebraic approach is complementary to existing geometric methods, and solves the problem for any number of arbitrary signal states with arbitrary prior probabilities. It has long been known that the minimum-error probability is given by the trace of the Lagrange operator $\mathrm{\Gamma }$. The remarkable feature of our approach is the central role played not by $\mathrm{\Gamma }$, but by its inverse.

We consider three modes $A$, $B$, and $C$ and derive monogamy inequalities that constrain the distribution of bipartite continuous variable Einstein-Podolsky-Rosen entanglement amongst the three modes. The inequalities hold without the assumption of Gaussian states, and are based on measurements of the quadrature phase amplitudes $X_i$ and $P_i$ at each mode $i=A,B,C$. The first monogamy inequality involves the well-known quantity $D_{IJ}$ defined by Duan-Giedke-Cirac-Zoller as the sum of the variances of $(X_I-X_J)/2$ and $(P_I+P_J)/2$ where $[X_I,P_J]={\delta }_{IJ}$. Entanglement between $I$ and $J$ is certified if $D_{IJ}<1$. A second monogamy inequality involves the more general entanglement certifier ${\text{Ent}}_{IJ}$ defined as the normalized product of the variances of $X_I-g{X}_J$ and $P_I+g{P}_J$, where $g$ is a real constant. The monogamy inequalities give a lower bound on the values of $D_{BC}$ and ${\text{Ent}}_{BC}$ for one pair, given the values $D_{BA}$ and ${\text{Ent}}_{BA}$ for the first pair. This lower bound changes in the absence of two-mode Gaussian steering of $B$. We illustrate for a range of tripartite entangled states, identifying regimes of saturation of the inequalities. The monogamy relations explain without the assumption of Gaussianity the experimentally observed saturation at $D_{AB}=0.5$ where there is symmetry between modes $A$ and $C$.

Small positively charged gold clusters have been found to emit thermal radiation at a very high rate, with time constants ranging from one to $35\mu \mathrm{s}$ for ${{\mathrm{Au}}_n}^{+}$ ($n=6\text{–}13,15$). For sizes $n=14,16\text{–}20$ the radiation occurs on much longer time scales. Strong thermal suppression of the population of higher-lying states puts constraints on the possible energies of excited states that can contribute to the radiation. Taking that into account, an evaluation of the experimentally determined rate constants shows that the strong radiation originates from thermally excited low-lying electronic states hitherto not observed. The origin of these states is discussed and two possibilities are suggested: one is related to electron correlation and electron pairing, and the other results from thermal shape fluctuations.

We propose to build a bad-cavity laser using forbidden transitions in large ensembles of cold ions that form a Coulomb crystal in a linear Paul trap. This laser might realize an active optical frequency standard able to serve as a local oscillator in next-generation optical clock schemes. In passive optical clocks, large ensembles of ions appear less promising, as they suffer from inhomogeneous broadening due to quadrupole interactions and micromotion-related shifts. In bad-cavity lasers, however, the radiating dipoles can synchronize and generate stable and narrow-linewidth radiation. Furthermore, for specific ions, micromotion-induced shifts can be largely suppressed by operating the ion trap at a magic frequency. We discuss the output radiation properties and perform quantitative estimations for lasing on the ${}^3{D}_2\to {}^1{S}_0$ transition in ${}^{176}\mathrm{Lu}{}^{+}$ ions in a spherically symmetric trap.

The exact time-evolution operator of an atom in the presence of a strong laser field is expressed using the phase-space path integral. Presenting this result in the form of a perturbative expansion in the effective interaction of the electron with the rest of the atom enables straightforward derivation of the well-known strong-field approximation and its higher-order corrections. Alternatively, one can use this exact result to obtain a semiclassical approximation by expansion in powers of small fluctuations around the classical trajectories. We present a derivation of such a semiclassical approximation. The obtained result for the momentum-space matrix element of the total time-evolution operator can be useful for studying various processes in strong-field physics. Using the example of above-threshold ionization, it is shown how this approximation can be applied to laser-induced processes. More attention is devoted to the laser-assisted scattering. Using the example of few-cycle laser-pulse-assisted electron-atom potential scattering, we show similarities and differences between the semiclassical and the strong-field approximations. For low energies, the semiclassical scattering cross section is modified and there are trajectories along which the electron is temporarily captured by the atomic potential. Applying stationary-phase method to the integral over the scattering time, we clearly identified relevant semiclassical electron trajectories.

We propose a two-step experimental protocol to directly engineer Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) states in a cold two-component Fermi gas loaded into a quasi-one-dimensional trap. First, one uses phase imprinting to create a train of domain walls in a superfluid with equal number of $\uparrow$- and $\downarrow$-spins. Second, one applies a radio-frequency sweep to selectively break Cooper pairs near the domain walls and transfer the $\uparrow$-spins to a third spin state, which does not interact with the $\uparrow$- and $\downarrow$-spins. The resulting FFLO state has exactly one unpaired $\downarrow$-spin in each domain wall and is stable for all values of domain-wall separation and interaction strength. We show that the protocol can be implemented with high fidelity at sufficiently strong interactions for a wide range of parameters available in present-day experimental conditions.

Within the second-quantization framework, we develop a formalism for describing a spatially multimode optical field diffracted through a spatial mask and show that this process can be described as an effective interaction between various spatial modes. We demonstrate a method to calculate the quantum state in the diffracted optical field for any given quantum state in the incident field. We also give several additional examples of how the theory works, for various quantum input states, which may be easily tested in the laboratory, including two single-mode squeezed vacuums, single- and two-photon inputs, where we show that the diffraction process produces a two-mode squeezed vacuum, number-path entanglement, and a Hong-Ou-Mandel-like effect analogous to that of a beam splitter.

On the basis of a quantum microscopic approach we study the dynamics of the afterglow of a dilute Gaussian atomic ensemble excited by pulsed radiation. Taking into account the vector nature of the electromagnetic field we analyze in detail the angular and polarization distribution of single-photon superradiance of such an ensemble. The dependence of the angular distribution of superradiance on the length of the pulse and its carrier frequency as well as on the size and the shape of the atomic clouds is studied. We show that there is substantial dependence of the superradiant emission on the polarization and the direction of fluorescence. We observe essential peculiarities of superradiance in the region of the forward diffraction zone and in the area of the coherent backscattering cone. We demonstrate that there are directions for which the rate of fluorescence is several times more than the decay rate of the timed-Dicke state. We show also that single-photon superradiance can be excited by incoherent excitation when atomic polarization in the ensemble is absent. Besides a quantum microscopic approach, we analyze single-photon superradiance on the basis of the theory of incoherent multiple scattering in optically thick media (random walk theory). In the case of very short resonant and long nonresonant pulses we derive simple analytical expressions for the decay rate of single-photon superradiance for incoherent fluorescence in an arbitrary direction.

We study the spontaneous decay of an impurity coupled to a linear array of bosonic cavities forming a single-band photonic waveguide. The average frequency of the emitted photon is different from the frequency for single-photon resonant scattering, which perfectly matches the bare frequency of the excited state of the impurity. We study how the energy of the excited state of the impurity influences the spatial profile of the emitted photon. The farther the energy is from the middle of the photonic band, the farther the wave packet is from the causal limit. In particular, if the energy lies in the middle of the band, the wave packet is localized around the causal limit. Besides, the occupation of the excited state of the impurity presents a rich dynamics: it shows an exponential decay up to intermediate times, this is followed by a power-law tail in the long-time regime, and it finally reaches an oscillatory stationary regime. Finally, we show that this phenomenology is robust under the presence of losses, both in the impurity and in the cavities.

We propose a bosonic Josephson junction (BJJ) in two nonlinear mechanical resonators coupled through two-phonon exchange interaction induced by quadratic optomechanical couplings. The nonlinear dynamical equations and effective Hamiltonian are derived to describe behaviors of the BJJ. We show that the BJJ can work in two different dynamical regimes: Josephson oscillation and macroscopic self-trapping. The system can transfer from one regime to the other one when the self-interaction and asymmetric parameters exceed their critical values. We show that the transition from Josephson oscillation to macroscopic self-trapping can be induced by the phonon damping of the asymmetric BJJ. Our results open up a way to demonstrate BJJ with two-phonon exchange interaction and might be applied to other systems.

Through rigorous simulations, the light scattering induced optical binding of one-dimensional (1D) dielectric photonic crystals is studied. The optical forces corresponding to the pass band, band gap, and band edge are qualitatively different. It is shown that light can induce self-organization of dielectric slabs into stable photonic crystals, with its lower band edge coinciding with the incident light frequency. Incident light at normal and oblique incidence and photonic crystals with parity-time symmetry are also considered.

The novel effect of self-excitation of an atomic beam propagating above a metal surface is predicted and a theory is developed. Its underlying mechanism is positive feedback provided by the reflective surface for the atomic polarization. Under certain conditions the atomic beam flying in the near field of the metal surface acts as an active device that supports sustained atomic dipole oscillations, which generate, in their turn, an electromagnetic field. This phenomenon does not exploit stimulated emission and therefore does not require population inversion in atoms. An experiment with Rydberg atoms in which this effect should be most pronounced is proposed and the necessary estimates are given.

We show that two parties far apart can use shared entangled states and classical communication to align their coordinate systems with a very high fidelity. Moreover, compared with previous methods proposed for such a task, i.e., sending parallel or antiparallel pairs or groups of spin states, our method has the extra advantages of using single-qubit measurements and also being secure, so that third parties do not extract any information about the aligned coordinate system established between the two parties. The latter property is important in many other quantum information protocols in which measurements inevitably play a significant role.

We combined high-resolution Fourier-transform spectroscopy and large-scale electronic structure calculation to study energy and radiative properties of the high-lying $\left(3\right){}^1\mathrm{\Pi }$ and $\left(5\right){}^1\mathrm{\Sigma }^{+}$ states of the RbCs molecule. The laser-induced $\left(5\right){}^1\mathrm{\Sigma }^{+},\left(4\right){}^1\mathrm{\Sigma }^{+},\left(3\right){}^1\mathrm{\Pi }\to A\left(2\right){}^1\mathrm{\Sigma }^{+}\sim b\left(1\right){}^3\mathrm{\Pi }$ fluorescence (LIF) spectra were recorded by the Bruker IFS-125(HR) spectrometer in the frequency range $\nu \in [5500,10000]{\mathrm{cm}}^{-1}$ with the instrumental resolution of 0.03 ${\mathrm{cm}}^{-1}$. The rotational assignment of the observed LIF progressions, which exhibit irregular vibrational-rotational spacing due to strong spin-orbit interaction between $A{}^1\mathrm{\Sigma }^{+}$ and $b{}^3\mathrm{\Pi }$ states was based on the coincidences between observed and calculated energy differences. The required rovibronic term values of the strongly perturbed $A\sim b$ complex have been calculated by a coupled-channels approach for both ${}^{85}\mathrm{Rb}{}^{133}\mathrm{Cs}$ and ${}^{87}\mathrm{Rb}{}^{133}\mathrm{Cs}$ isotopologs with accuracy of about 0.01 ${\mathrm{cm}}^{-1}$, as demonstrated in A. Kruzins et al. [J. Chem. Phys. 141, 184309 (2014)]. The experimental energies of the upper $\left(3\right){}^1\mathrm{\Pi }$ and $\left(5\right){}^1\mathrm{\Sigma }^{+}$ states were involved in a direct-potential-fit analysis performed in the framework of inverted perturbation approach. Quasirelativistic ab initio calculations of the spin-allowed $\left(3\right){}^1\mathrm{\Pi },\left(5\right){}^1\mathrm{\Sigma }^{+}\to$ (1-4)${}^1\mathrm{\Sigma }^{+}$,(1-3)${}^1\mathrm{\Pi }$ transition dipole moments were performed. Radiative lifetimes and vibronic branching ratios of radiative transitions from the $\left(3\right){}^1\mathrm{\Pi }$ and $\left(5\right){}^1\mathrm{\Sigma }^{+}$ states were evaluated. To elucidate the origin of the $\mathrm{\Lambda }$-doubling effect in the $\left(3\right){}^1\mathrm{\Pi }$ state, the angular coupling $\left(3\right){}^1\mathrm{\Pi }$-(1-5)${}^1\mathrm{\Sigma }^{+}$ electronic matrix elements were calculated and applied for the relevant $q$-factors estimate. The intensity distributions simulated for the particular $\left(5\right){}^1\mathrm{\Sigma }^{+}$;$\left(3\right){}^1\mathrm{\Pi }\to A\sim b$ LIF progressions have been found to be remarkably close to their experimental counterparts.

Collisions with background gas can perturb the transition frequency of trapped ions in an optical atomic clock. We develop a nonperturbative framework based on a quantum channel description of the scattering process and use it to derive a master equation which leads to a simple analytic expression for the collisional frequency shift. As a demonstration of our method, we calculate the frequency shift of the ${\mathrm{Sr}}^{+}$ optical atomic clock transition due to elastic collisions with helium.

We present a theoretical and experimental study of the angular and temperature dependence of the photon pairs produced by spontaneous parametric down-conversion in a periodically poled KTP crystal. In the experiment, two detectors are placed at different angles in the emitted light, and the detected photon pair rate is measured as a function of one angle or of crystal temperature. In the theoretical work, exact results for the pair rates are obtained through importance-sampled numerical integration of the fourth-order coherence function over regions representing the experimental integration parameters. Conditions studied range from well-resolved results in which detector angular and filter bandwidth integration effects are negligible, to other cases in which such effects are large and pair rates exceed ${10}^5{\mathrm{s}}^{-1}$. Throughout these cases, good agreement is often seen between experimental and theoretical results, while some differences that are noted provide insight into the actual crystal quasi-phase-matching function.

The light shift caused by an optical dipole force trap on a single ${}^{87}\mathrm{Rb}$ atom was recently studied by Shih and Chapman [Phys. Rev. A 87, 063408 (2013)] using a dipole-matrix-element-based approach. A separate study by Neuzner et al. [Phys. Rev. A 92, 053842 (2015)] considered the same system using a polarizability-based approach. We find that the results of these two studies do not agree, which we ascribe to an error in the theoretical part of Shih and Chapman's paper. We correct this error, offer an alternative formulation for the energy-level shift using the matrix-element-based approach, and find good agreement between our predictions and those obtained with the polarizability-based method. Furthermore, our predictions are in better agreement with Shih and Chapman's experimental results in comparison to their predictions. In contrast to the polarizability-based method, our formulation can be easily extended to different trapping wavelengths and atomic species.