An exact generalization of the Ramsey transition probability is derived to improve ultrahigh precision measurement and quantum state engineering when a particle is subjected to independently-tailored separated oscillating fields. The phase shift accumulated at the end of the interrogation scheme and associated with the particle wave function is offering a very high-level control of quantum states throughout various laser parameters conditions. The generalized hyper-Ramsey resonance based on independent manipulation of interaction time, field amplitude, phase, and frequency detuning is presented to increase performances in the next generation of atomic, molecular, and nuclear clocks, to upgrade high-resolution frequency measurement in Penning trap mass spectrometry and for a better control of light-induced frequency shifts in matter-wave interferometer or quantum information processing.

We present a theoretical study of the ground state of the BCS-BEC crossover in dilute two-dimensional Fermi gases. While the mean-field theory provides a simple and analytical equation of state, the pressure is equal to that of a noninteracting Fermi gas in the entire BCS-BEC crossover, which is not consistent with the features of a weakly interacting Bose condensate in the BEC limit and a weakly interacting Fermi liquid in the BCS limit. The inadequacy of the two-dimensional mean-field theory indicates that the quantum fluctuations are much more pronounced than those in three dimensions. In this work, we show that the inclusion of the Gaussian quantum fluctuations naturally recovers the above features in both the BEC and the BCS limits. In the BEC limit, the missing logarithmic dependence on the boson chemical potential is recovered by the quantum fluctuations. Near the quantum phase transition from the vacuum to the BEC phase, we compare our equation of state with the known grand canonical equation of state of two-dimensional Bose gases and determine the ratio of the composite boson scattering length $a_B$ to the fermion scattering length $a_{2\mathrm{D}}$. We find $a_B\simeq 0.56a_{2\mathrm{D}}$, in good agreement with the exact four-body calculation. We compare our equation of state in the BCS-BEC crossover with recent results from the quantum Monte Carlo simulations and the experimental measurements and find good agreements.

We study Majorana fermions (MFs) in quasi-one dimensional (quasi-1D) and higher-dimensional fermionic optical lattices with a strictly 1D spin-orbit coupling, which has already been realized in cold atom experiments. We show that when the superfluid order parameters are homogeneous and are enforced to be identical along different chains, there are multiple MFs at each end with or without an experimentally tunable in-plane Zeeman field $V_y$. For $V_y=0$ the multiple MFs are topologically protected by a chiral symmetry; however, for $V_y\ne 0$ the existence of multiple MFs is related to the peculiar spectrum properties of the system despite the broken chiral symmetry. In the generalization to higher dimensions, the multiple MFs form a zero-energy flat band. Furthermore, when the superfluid order parameters are solved self-consistently, the multiple MFs are usually destroyed because of the inhomogeneous order parameters of either Bardeen-Cooper-Schrieffer ($V_y=0$) type or Fulde-Ferrell ($V_y\ne 0$) type. Our results are useful to guide the experimentalists on searching for MFs in ultracold spin-orbit coupled fermionic superfluids.

We propose a scheme to store the spin-nematic squeezing in a spinor Bose-Einstein condensate by applying periodic microwave pulses. For a proper pulse period and phase shift, the squeezing can be enhanced and maintained for a long time, which realizes the storage of the maximal squeezing. We also propose a method to generate the spin-nematic squeezed vacuum, which is associated with negligible occupation of the squeezed modes, through an adiabatic sweep of the magnetic field. It is shown that the method can be readily implemented for both ferromagnetic and antiferromagnetic condensates.

We investigate the behavior of a harmonically trapped system consisting of an impurity in a dilute ideal Bose gas after the boson-impurity interaction is suddenly switched on. As a theoretical framework, we use a field-theory approach in the space-time domain within the $T$-matrix approximation. We establish the form of the corresponding $T$ matrix and address the dynamical properties of the system. As a numerical application, we consider a simple system of a weakly interacting impurity in one dimension where the interaction leads to oscillations of the impurity density. Moreover, we show that the amplitude of the oscillations can be driven by periodically switching the interaction on and off.

We have considered optical beams with phase singularity and experimentally verified that these beams, although classical, have properties of two-mode entanglement in quantum states. We have observed the violation of Bell's inequality for continuous variables using the Wigner distribution function (WDF) proposed by P. Chowdhury et al. [Phys. Rev. A 88, 013830 (2013)]. Our experiment establishes an alternate form of Bell's inequality in terms of the WDF which can be used for classical as well as quantum systems.

Accelerating a light beam makes a particle move along a curvilinear trajectory. We show that the curvature of the trajectory causes a special kind of nonconservative force, which is called a curvilinear force. We obtain the expression for this force acting on a spherical particle in the Rayleigh approximation and determine its value for several types of accelerating fields including Bessel, Airy, and arbitrary-trajectory beams. We anticipate applications of the curvilinear forces in optical micromanipulation with accelerating beams.

We propose and analyze a scheme for photon trapping in an optical resonator coupled with two-level atoms. We show that when the cavity is excited by two identical light fields, one from each end of the cavity, the output light from the cavity is suppressed while the intracavity light field is nearmaximum due to the excitation of the polariton state of the coupled cavity and atom system. We also present methods for the direct probing of the trapped polariton state. The photon trapping is manifested by the destructive interference of the transmitted light and the incident light, which is conditioned on the presence of incoherent processes such as spontaneous decay of the atomic excitation of the polariton state. Such photon trapping is quite generic and should be observable experimentally in a variety of cavity quantum electrodynamics systems.

QED cascades in an intense electromagnetic field can occur if the dynamical quantum parameter $\chi$ of a seed electron, which in Compton units coincides with the electron proper acceleration, attains the order of unity. We derive a general expression for $\chi$ of an initially slow electron in an arbitrary electromagnetic field for a time range $t\ll 1/\omega$, where $\omega$ is the field carrier frequency. Using this formula, we consider a special field configuration of multiple colliding focused laser beams and optimize it to provide cascade development at laser power below 10 PW and intensity of the order of ${10}^{23}\mathrm{W}/{\mathrm{cm}}^2$. Such parameters of the beams will be obtained with a new generation of laser facilities, particularly the ELI Beamlines, in the coming years.

We propose a general formulation of the renormalization group (RG) as a family of quantum channels which connect the microscopic physical world to the observable world at some scale. By endowing the set of quantum states with an operationally motivated information geometry, we induce the space of Hamiltonians with a corresponding metric geometry. The resulting structure allows one to quantify information loss along RG flows in terms of the distinguishability of thermal states. In particular, we introduce a family of functions, expressible in terms of two-point correlation functions, which are nonincreasing along the flow. Among those, we study the speed of the flow and its generalization to infinite lattices.

By proposing device-independent protocols, Pironio et al. [Nature (London) 464, 1021 (2010)] and Colbeck et al. [Nat. Phys. 8, 450 (2012)] proved that new randomness can be generated by using perfectly free random sources or partially free ones as seed. Subsequently, Li et al. [Phys. Rev. A 84, 034301 (2011)] studied this topic in the framework of semi-device-independent and proved that new randomness can be obtained from perfectly free random sources. Here we discuss whether and how partially free random sources bring us new randomness in a semi-device-independent scenario. We propose a semi-device-independent randomness expansion protocol with partially free random sources and obtain the condition that the partially free random sources should satisfy to generate new randomness. In the process of analysis, we acquire a two-dimensional quantum witness. Furthermore, we get the analytic relationship between the generated randomness and the two-dimensional quantum witness violation.

For years, inelastic, fine-structure-changing collisions between excited alkali-metal atoms and noble-gas perturbers have been a source of information on the alkali-metal–noble-gas interaction. Here, we consider the role of elastic fine-structure-mixing collisions on alkali-metal absorption cross sections. Specifically, we consider the four optical hyperfine transitions of the $D_1$ absorption spectrum for ${}^{87}\mathrm{Rb}$, and in particular the doublet corresponding to $5{}^{2}S_{1/2}(F_g=2)-5{}^{2}P_{1/2}(F_e=1,2)$ transitions. Although ideally the amplitudes of the doublet's absorption cross sections are identical, we find that fine-structure mixing of $D_2$ oscillator strength into the $D_1$ spectrum breaks the cross sections' equality and leads to doublet asymmetry. We obtain a fine-structure mixing parameter $\lambda$ of $(5.4\pm 0.3)\times {10}^{-21}\mathrm{c}{\mathrm{m}}^3$, and estimate a $5{}^{2}P_{1/2}$ hyperfine-splitting density shift $\zeta$ in the ${}^{87}\mathrm{Rb}$-Xe system of $+0.71\pm 0.03\mathrm{GHz}/\mathrm{amagat}$. These results have implications for spectroscopic applications of the ${}^{87}\mathrm{Rb}$ isoclinic point, which we consider as part of our conclusions.

We present effects of electron energy transfer by electron collisions on high-order-harmonic generation (HHG) in molecular sequential double ionization by intense circularly polarized laser pulses. Results from numerical solutions of time-dependent Schrödinger equations for extended (large internuclear distance) ${\mathrm{H}}_2$ where electrons are entangled and hence delocalized by exchange show that HHG with cutoff energy up to $I_p+24U_p$ can be obtained, where $I_p$ is the molecule ionization potential and $U_p=I_0/4{\omega }_0^2$ (in atomic units) is the ponderomotive energy for pulse intensity $I_0$ and frequency ${\omega }_0$. A time-frequency analysis is employed to identify electron collisions for the generation of harmonics. Extended HHG arises from electron energy exchange, which agrees well with the prediction of a classical two electron collision model. Results for nonsymmetric ${\mathrm{HHe}}^{+}$ where initially electrons are localized on He are also compared and confirm the role of initial electron delocalization via entanglement for obtaining extended HHG plateaus.

We present a cluster Gutzwiller mean-field study for ground states and time-evolution dynamics in the Bose-Hubbard ladder (BHL), which can be realized by loading Bose atoms in double-well optical lattices. In our cluster mean-field approach, we treat each double-well unit of two lattice sites as a coherent whole for composing the cluster Gutzwiller ansatz, which may remain some residual correlations in each two-site unit. For an unbiased BHL, in addition to conventional superfluid phase and integer Mott insulator phases, we find that there are exotic fractional insulator phases if the interchain tunneling is much stronger than the intrachain one. The fractional insulator phases cannot be found by using a conventional mean-field treatment based upon the single-site Gutzwiller ansatz. For a biased BHL, we find there appear single-atom tunneling and interaction blockade if the system is dominated by the interplay between the on-site interaction and the interchain bias. In the many-body Landau-Zener process, in which the interchain bias is linearly swept from negative to positive or vice versa, our numerical results are qualitatively consistent with the experimental observation [Nat. Phys. 7, 61 (2011)]. Our cluster bosonic Gutzwiller treatment is of promising perspectives in exploring exotic quantum phases and time-evolution dynamics of bosonic particles in superlattices.

We extend the theory of matter-wave interferometry of pointlike particles to nonspherical objects by taking the orientational degrees of freedom into account. In particular, we derive the grating transformation operator, which maps the impinging state onto the outgoing state, for a general, orientation-dependent interaction potential between the grating and the molecule. The grating operator is then worked out for the diffraction of symmetric top molecules from standing light waves, and the resulting interference pattern is calculated in the near field. This allows us to identify a signature of the orientational degrees of freedom in near-field matter-wave experiments.

We report branches of explicit expressions for nonlinear modes in parity-time $\left(\mathcal{PT}\right)$-symmetric potentials of several types. For the single-well and double-well potentials the found solutions are two-parametric and appear to be stable even when the $\mathcal{PT}$ symmetry of respective underlying linear models is broken. Based on the examples of these solutions we describe an algorithm of excitation of a stable nonlinear mode in a model whose linear limit is unstable. The method is based on the adiabatic change of the control parameter driving the mode along a branch bifurcating from a stable linear mode. The suggested algorithm is confirmed by extensive numerical simulations.

We study two fundamental transitions from the ground state ${}^{1}S_0$ to ${}^{1}P_1$ ($w$ line) and ${}^{3}P_1$ ($y$ line) in heliumlike ${\mathrm{Kr}}^{34+}$ by resonant single-photon excitation using an electron-beam ion trap and monochromatic x rays at PETRA III. Our results for the transition energies $E\left(w\right)=13114.47\left(14\right)$ eV and $E\left(y\right)=13026.15\left(14\right)$ eV are in excellent agreement with quantum electrodynamics calculations, but disagree for $w$ with the average of the hitherto reported experimental results ${\overline{E}}_{\mathrm{Lit}}\left(w\right)=13115.15\left(17\right)$ eV. Independently of any energy calibration, we obtain a value $E\left(w\right)/E\left(y\right)=1.006780\left(7\right)$, also in consistency with predictions.

We describe forms of adiabatic transport that arise for dressed-state atoms in optical lattices. Focusing on the limit of weak tunnel-coupling between nearest-neighbor lattice sites, we explain how adiabatic variation of optical dressing allows control of atomic motion between lattice sites: allowing adiabatic particle transport in a direction that depends on the internal state, and force measurements via spectroscopic preparation and readout. For uniformly filled bands these systems display topologically quantized particle transport. An implementation of the dressing scheme using optical transitions in alkaline-earth atoms is discussed as well as its favorable features for precise force sensing.

Based on a microscopic approach, we propose a Lagrangian for the combined system of a rotating dielectric nanoparticle above a plane surface in the presence of electromagnetic vacuum fluctuations. In the framework of canonical quantization, the electromagnetic vacuum field is quantized in the presence of dielectric fields describing the nanoparticle and a semi-infinite dielectric with planar interface. The radiative heat power absorbed by the rotating nanoparticle is obtained and the result is in agreement with previous results when the rotational frequency ${\omega }_0$ of the nanoparticle is zero or much smaller than the relaxation frequency of the dielectrics. The well-known near-field effect is reexamined and discussed in terms of the rotational frequency. The radiative heat power absorbed by the nanoparticle for well-known peak frequencies is plotted in terms of the rotational frequency ${\omega }_0$ showing an interesting effect resembling a phase transition around a critical frequency $\mathrm{\Gamma }$, determined by the relaxation frequency of the dielectrics.

We construct the Runge-Lenz vector and the symmetry algebra of the rational Calogero-Coulomb problem using the Dunkl operators. We reveal that they are proper deformations of their Coulomb counterpart. Together with similar correspondence between the Calogero oscillator and oscillator models, this observation permits the claim that most of the properties of the Coulomb and oscillator systems can be lifted to their Calogero-extended analogs by the proper replacement of the momenta by the Dunkl momenta operators.