We suggest the generation of photon pairs in a thermally induced nonlinear periodically poled silica fiber by spontaneous parametric down-conversion. Photons are generated directly in eigenstates of optical angular momentum. Photons in a pair can be entangled in these states as well as in frequencies. We identify suitable spatial and polarization modes giving an efficient nonlinear interaction. By changing the pump field properties both narrow- and broadband down-converted fields can be obtained.

We describe theoretically the process of spontaneous parametric down-conversion in quadratic nonlinear waveguide arrays in the presence of linear loss. We derive a set of discrete Schrödinger-type equations for the biphoton wave function and the wave function of one photon when the other photon in a pair is lost. We demonstrate effects arising from loss-affected interference between the generated photon pairs and show that nonlinear waveguide arrays can serve as a robust loss-tolerant integrated platform for the generation of entangled photon states with nonclassical spatial correlations.

We theoretically demonstrate second-order Talbot effect (SOTE) based on entangled photon pairs. The photon pairs are generated from the spontaneous parametric four-wave mixing (SPFWM) process in a cold atomic medium and can be taken as the imaging light in order to realize coincidence recording. A strong standing wave is used to create the electromagnetically induced grating in the entangled photon pairs channels. By changing the frequency detuning of the standing wave or the other optical fields participating in the process, we can manipulate the contrast of the second-order Talbot image. We use the second-order correlation function and the dressed-state picture to explain the SOTE occurring in the SPFWM process. Moreover, we demonstrate the scheme for SOTE based on the spatially correlated twin beams generated from the SPFWM process with injection. This scheme provides a convenient detection proposal for the SOTE at the cost of the image contrast. Compared to the previous self-imaging schemes, the present schemes have the characteristic of controllable image contrast and of nonlocal imaging, and thus, they might broaden their applications in imaging techniques and find applications in quantum lithography.

We theoretically investigate mode broadening of a high-$Q$ optical whispering-gallery microcavity coupled to a single or multiple dielectric or plasmonic subwavelength particles. The result shows that backscattering contributes dominantly to the mode broadening in both transmission and reflection spectra for dielectric particles binding on the microcavity surface, while absorption also plays an important role for lossy nanoparticles. The mode broadening induced by nanoparticles holds great potential in optical biosensing. For instance, by monitoring the change of mode linewidth, a single 11-nm-radius spherical polystyrene nanoparticle is detectable. This detection breaks through the detection limit of the mode-splitting method using a passive cavity and remains immune to various noises, such as thermal fluctuations and frequency drifts of the probe laser. Finally, the mode broadening is demonstrated to be particularly suitable for detecting lossy nanoparticles, e.g., plasmonic particles.

Optomechanics allows the transduction of weak forces to optical fields, with many efforts approaching the standard quantum limit. We consider force sensing in a mirror-in-the-middle optomechanical setup and use two coupled cavity modes originated from normal mode splitting for separating pump and probe fields. We find that this two-mode model can be reduced to an effective single-mode model if we drive the pump mode strongly and detect the signal from the weak probe mode. We show that the optimal force sensitivity at zero frequency (dc) beats the standard quantum limit via squeezing and is limited by mechanical thermal noise and optical losses. We also find that the bandwidth is proportional to the cavity damping in the resolved sideband regime. Finally, the squeezing spectrum of the output signal is calculated and it shows that almost perfect squeezing at dc is possible by using a high-quality factor and high-frequency mechanical oscillator. Considering a homodyne measurement efficiency of 99%, the squeezing will be limited to 23 dB, with requires input power ${10}^{-2}$ smaller than conventional single-mode optomechanical systems.

We investigate the dissipative influence of environmental fluctuations on the dynamics of driven quantum systems at an avoided crossing. We derive two simple approximative equations valid for weak system-bath coupling and compare results for the dissipative Landau-Zener problem with numerically exact results. Very good agreement is found for slow, i.e., adiabatic, driving. Specifically, the minimum in the Landau-Zener probability resulting from the competition of driving and dissipation is well described. For system-bath couplings and temperatures, where this minimum is observed in the adiabatic driving regime, good agreement is also observed for fast driving when the dynamics tends toward nonadiabatic behavior. Otherwise, however, for large temperatures and fast driving our approximation fails even for weak system-bath couplings, for which an undriven system is still accurately described by weak-coupling approximations.

Heisenberg's uncertainty principle is quantified by error-disturbance tradeoff relations, which have been tested experimentally in various scenarios. Here we shall report various error-disturbance tradeoff relations by decomposing the measurement errors and disturbance into two different components, namely, operator bias and fuzziness. Our uncertainty relations reveal the tradeoffs between these two components of errors, and imply various conditionally valid error-tradeoff relations for the unbiased and projective measurements. We also design a quantum circuit to measure the two components of the error and disturbance.

We propose a method for deterministic generation of entanglement between a quantum-dot spin and a photon. Entanglement is established by an elastic scattering event from a cavity that is strongly coupled to a singly charged quantum dot. Due to the elastic nature of the interaction, the energy of the photon does not become entangled with the quantum dot, eliminating the need for temporal postselection. We derive an analytical expression for fidelity of the generated entangled state and investigate its behavior under realistic experimental conditions. We show that entanglement fidelities exceeding 0.974 can be realized using currently achievable quantum-dot cavity quantum electrodynamics systems.

We study the $H^{3\times N}$ hybrid entanglement between charge and vibrational modes in a triple-quantum-dot shuttle system. Three quantum dots are linearly connected, with the outer dots fixed and the central dot oscillating, described as a quantum harmonic oscillator with oscillation modes that are entangled with the electronic states of the quantum dots. The entangled states are characterized by the Schmidt number as a function of the parameters of the system: detuning and inverse tunneling length. We show that at steady state, as a function of detuning, the excited states of lower energy present Bell-type entanglement $2\times N$, with the participation of two quantum dots, while the more energetic excited states present $3\times N$ entanglement, with the participation of three quantum dots. In the stationary regime, we find qualitative relationships between the maxima of the electronic current and the Schmidt number. Also, the time evolution of the degree of entanglement for a particular initial condition is studied in the presence of a time-dependent electric field and we evaluate the effects on entanglement of the condition of coherent destruction of tunneling.

We consider systems of two and three qubits, mutually coupled by Heisenberg-type exchange interaction and interacting with external laser fields. We show that these systems allow one to create maximally entangled Bell states, as well as three-qubit Greenberger-Horne-Zeilinger and $W$ states. In particular, we point out that some of the target states are the eigenstates of the initial bare system. Due to this, one can create entangled states by means of pulse area and adiabatic techniques, when starting from a separable (nonentangled) ground state. On the other hand, for target states, not present initially in the eigensystem of the model, we apply the robust stimulated Raman adiabatic passage and $\pi$ pulse techniques, that create desired coherent superpositions of nonentangled eigenstates.

We develop a theoretical framework for the quasi-low-dimensional confinement-induced resonances (CIRs) of particles with three-dimensional two-body interactions describable by the Huang-Yang pseudopotential. Using this approach, we analytically obtain the universal properties of dipolar CIRs in quasi-one-dimensional (quasi-1D) waveguides. We also show that the tilting angle between the dipole moment and the waveguide can be used as a control knob for scatterings in quasi-1D geometry. More importantly, the tilting-angle-induced dipolar CIRs in quasi-1D Cr, Er, and Dy atomic gases are experimentally detectable.

We show that Jaynes-Cummings dynamics can be observed in mesoscopic atomic ensembles interacting with a classical electromagnetic field in the regime of a Rydberg blockade where the time dynamics of the average number of Rydberg excitations in mesoscopic ensembles displays collapses and revivals typical of this model. As the frequency of Rabi oscillations between collective states of Rydberg-blockaded ensembles depends on the number of interacting atoms, for randomly loaded optical dipole traps, we predict collapses and revivals of Rabi oscillations. We have studied the effects of finite interaction strengths and a finite laser linewidth on the visibility of the revivals. We have shown that observation of collapses and revivals of Rabi oscillations can be used as a signature of the Rydberg blockade without the need to measure the exact number of Rydberg atoms.

We study a spin-orbit (SO)-coupled hyperfine spin-1 Bose-Einstein condensate (BEC) in a quasi-one-dimensional trap. For an SO-coupled BEC in a one-dimensional box, we show that in the absence of the Rabi term, any nonzero value of SO coupling will result in a phase separation among the components for a ferromagnetic BEC, like ${}^{87}\mathrm{Rb}$. On the other hand, SO coupling favors miscibility in a polar BEC, like ${}^{23}\mathrm{Na}$. In the presence of a harmonic trap, which favors miscibility, a ferromagnetic BEC phase separates, provided that the SO-coupling strength and number of atoms are greater than some critical value. The Rabi term favors miscibility irrespective of the nature of the spin interaction: ferromagnetic or polar.

A two-dimensional Bose-Einstein condensate (BEC) split by a radial potential barrier is investigated. We determine on an accurate many-body level the system's ground-state phase diagram as well as a time-dependent phase diagram of the splitting process. Whereas the ground state is condensed for a wide range of parameters, the time-dependent splitting process leads to substantial fragmentation. We demonstrate the dynamical fragmentation of a BEC despite its ground state being condensed. The results are analyzed using a mean-field model and suggest that a large manifold of low-lying fragmented excited states can significantly impact the dynamics of trapped two-dimensional BECs.

The collective excitations of a zero-temperature, spin-polarized, harmonically trapped, two-dimensional dipolar Fermi gas are examined within the Thomas-Fermi–von Weizsäcker hydrodynamic theory. We focus on repulsive interactions and investigate the dependence of the excitation frequencies on the strength of the dipolar interaction and particle number. We find that the mode spectrum can be classified according to bulk modes, whose frequencies are shifted upward as the interaction strength is increased, and an infinite ladder of surface modes, whose frequencies are independent of the interactions in the large particle limit. We argue quite generally that it is the local character of the two-dimensional energy density that is responsible for the insensitivity of surface excitations to the dipolar interaction strength and not the precise form of the equation of state. This property will not be found for the collective excitations of harmonically trapped, dipolar Fermi gases in one and three dimensions, where the energy density is manifestly nonlocal.

A light-matter interaction modified by the material environment is one of the central topics in quantum electrodynamics. While a strong coupling between a single emitter and a cavity and the Markovian (exponential) relaxation regime are most straightforwardly covered by theory, real physical systems that include also various line broadening effects may possess a much more complicated behavior. Here we propose a theoretical framework to account for nonradiative interaction effects in emission in photonic and plasmonic cavities. The quantum electrodynamics model formulated via a stochastic Hamiltonian approach has been developed with nonradiative line broadening introduced via the Kubo oscillator model. The impact of competing radiative and nonradiative processes on the emitter dynamics has been studied, showing that nonradiative relaxations, having significant impact on processes in high-$Q$ photonic cavities, are much less influential in the plasmonic regime. The developed theoretical framework is not restricted to the emitter in a cavity example, but represents a general tool for multiple stochastic Hamiltonian evolution, important for various types of interactions where either classical or quantum noise is present.

We show how interference effects are responsible for manipulating the output electromagnetic field of an optical microresonator in the good-cavity limit. The system of interest consists of a moderately strongly pumped two-level emitter embedded in the optical cavity. When an additional weaker laser of the same frequency is pumping the combined system through one of the resonator's mirrors then the output-cavity-electromagnetic field can be almost completely suppressed or enhanced. This is due to the interference among the scattered light by the strongly pumped atom into the cavity mode and the incident weaker laser field. The result applies to photonic crystal environments as well.

The resonant quantum dynamics of an excited two-level emitter is investigated via classical modulation of its transition frequency while simultaneously the radiator interacts with a broadband electromagnetic field reservoir. The frequency of modulation is selected to be of the order of the bare-state spontaneous decay rate. In this way, one can induce quantum interference effects, and consequently, quantum coherences among multiple decaying transition pathways. Depending on the modulation depth and its absolute phase, both the spontaneous emission and the frequency shift may be conveniently modified and controlled.

We propose a scheme to efficiently manipulate optomechanical systems into and out of chaotic regimes. Here the optical system is coherently driven by a continuous-wave bichromatic laser field consisting of a pump field and a probe field, where the beat frequency of the bichromatic components plays an important role in controlling the appearance of chaotic motion and the corresponding chaotic dynamics. With state-of-the-art experimental parameters, we find that a broad chaos-absent window with sharp edges can be formed by properly adjusting the powers of the bichromatic input field. Moreover, the lifetime of the transient chaos and the chaotic degree of the optomechanical system can be well tuned simply by changing the initial phases of the bichromatic input field. This investigation may be useful for harnessing the optomechanical nonlinearity to manipulate rich chaotic dynamics and find applications in chaos-based communication.