The maximum amplitude of mechanical oscillators coupled to optical cavities is studied both analytically and numerically. The optical backaction on the resonator enables self-sustained oscillations whose limit cycle is set by the dynamic range of the cavity. The maximum attainable amplitude and the phonon generation quantum efficiency of the backaction process are studied for both unresolved and resolved cavities. Quantum efficiencies far exceeding one are found in the resolved sideband regime where the amplitude is low. On the other hand, the maximum amplitude is found in the unresolved system. Finally, the role of mechanical nonlinearities is addressed.

We propose a quantum memory for a single-photon wave packet in a superposition of two different colors, i.e., two different frequency components, using the electromagnetically induced transparency technique in a double-$\Lambda$ system. We examine a specific configuration in which the two frequency components are able to exchange energy through a four-wave mixing process as they propagate, so the state of the incident photon is recovered periodically at certain positions in the medium. We investigate the propagation dynamics as a function of the relative phase between the coupling beams and the input single-photon frequency components. Moreover, by considering time-dependent coupling beams, we numerically simulate the storage and retrieval of a two-frequency-component single-photon qubit.

We employ double quantum interference to propose a ground-state cooling scheme for a nanomechanical resonator coupled to a triple quantum dot (TQD), of which the third dot is driven by a microwave field. In our scheme, the carrier transition is diminished by the destructive interference (the occurrence of a dark state) arising from the coherent tunnelings of electrons among the three dots. Furthermore, the additional transition induced by the microwave field enables the system to possess double quantum interference effect. Under certain conditions, the processes which might increase one phonon through the blue sideband transitions are prohibited due to the double destructive interference analog to double electromagnetically induced transparency mechanism. Thus, both the carrier and blue sideband transitions are canceled. The cooling process occurs when the electron trapped in the dark state absorbs one phonon of the resonator through the transition from the dark state to the bright state and then to the excited state and finally tunnels to the drain. As a result, the phonon occupation can be reduced to zero in the ideal case and the resonator can be cooled down to its ground state with high efficiency even when the dephasing of the TQD is present.

We study theoretically the dynamics of collective excitations in one- and two-dimensional arrays of evanescent-wave coupled nonlinear photonic nanowires. This system shows a strong spatiotemporal coupling, which can be observed in its frequency-dependent reciprocal space. We have found that the first Brillouin zone of the system can be separated into two regions characterized by elliptic and hyperbolic nonlinear solutions. Different forms of soliton bullets, vortices, and $X$ waves are estimated, and the effect of the spatiotemporal coupling is identified as a spatiotemporal tilt of the moving solutions. A numerical analysis is performed to support the theoretical calculations.

We provide exact analytical solutions for the problem of time-optimal transfer of coherence from one spin-polarization to a threefold coherence in a trilinear Ising chain with a fixed energy available and subject to local controls with a non-negligible time cost. The time of transfer is optimal and consistent with a previous numerical result obtained assuming instantaneous local controls.

The analysis of traps, that is, locally but not globally optimal controls, for quantum control systems has attracted great interest in recent years. The central problem that has remained open is to demonstrate for a given system either the existence or the absence of traps. We prove the absence of traps and hence completely solve this problem for the important tasks of unconstrained manipulation of the transition probability and unitary gate generation in the Landau-Zener system, a system with a wide range of applications across physics, chemistry, and biochemistry. This finding provides an example of a controlled quantum system which is completely free of traps. We also discuss the impact of laboratory constraints due to decoherence, noise in the control pulse, and restrictions on the available controls, which, when being sufficiently severe, can produce traps.

We consider a mixture of two neutral cold Fermi gases with repulsive interactions. We show that in some region of the parameter space of the system the effective attraction between fermions of the same type can appear due to the exchange of collective excitations. This leads to the formation of BCS pairing in the case where bare interatomic interactions are repulsive.

We investigate two-dimensional turbulence in finite-temperature trapped Bose-Einstein condensates within damped Gross-Pitaevskii theory. Turbulence is produced via circular motion of a Gaussian potential barrier stirring the condensate. We systematically explore a range of stirring parameters and identify three regimes, characterized by the injection of distinct quantum vortex structures into the condensate: (A) periodic vortex dipole injection, (B) irregular injection of a mixture of vortex dipoles and co-rotating vortex clusters, and (C) continuous injection of oblique solitons that decay into vortex dipoles. Spectral analysis of the kinetic energy associated with vortices reveals that regime (B) can intermittently exhibit a Kolmogorov $k^{-5/3}$ power law over almost a decade of length or wave-number ($k$) scales. The kinetic energy spectrum of regime (C) exhibits a clear $k^{-3/2}$ power law associated with an inertial range for weak-wave turbulence and a $k^{-7/2}$ power law for high wave numbers. We thus identify distinct regimes of forcing for generating either two-dimensional quantum turbulence or classical weak-wave turbulence that may be realizable experimentally.

New technologies providing tightly focusing lenses and mirrors with large numerical apertures and electro-optic modulation of single photons are now available for the investigation of photon-atom interactions without a cavity. From the theoretical side, new models must be developed which take into account the intrinsic open system aspect of the problem as well as details about atomic relative positions and temporal (spectral) features of the pulses. In this paper, we investigate the generation of nonclassical correlations between two atoms in free space interacting with a quantized pulse containing just one single photon. For this purpose, we develop a general theoretical approach which allows us to find the equations of motion for single- and two-body atomic operators from which we obtained the system density operator. We show that one single photon is capable of promoting substantial entanglement between two initially ground-state atoms, and we analyze the dependence of these correlations on atomic relative positions (vacuum effects) and spectral features of the single-photon pulse.

The dissociative ionization of a N${}_2$O molecule is studied at an electron energy of 10 keV using the multiple-ion-coincidence imaging technique. The complete as well as the incomplete Coulomb explosion pathways for N${}_2$O${}^{2+}$ and N${}_2$O${}^{3+}$ ions are examined and identified. The precursor-specific relative partial ionization cross sections for resulting fragment ions are obtained. It is found that about 81.8$\%$ of single ionization, 17.8$\%$ of double ionization, and about 0.4$\%$ of triple ionization of the parent molecule contribute to the total fragment ion yield. Furthermore, the relative ionic fractions for ion-pair and ion-triple formation are also determined. The kinetic energy release distributions for different coincidence channels are obtained and compared with the available data at lower energies of electron and photon impacts and with that of high-energy ion impact. From the angular correlation studies of fragment ions, it is inferred that states with bent geometries are involved for most of the fragmentation channels of N${}_2$O${}^{2+}$ and N${}_2$O${}^{3+}$ ions. The concerted and/or sequential nature of the six dissociation pathways is also assigned. No other experimental or theoretical data exist in the literature to compare with the results obtained at the considered impact energy.

In this work we consider a system of spinless fermions with nearest and next-to-nearest neighbor repulsive Hubbard interactions on a honeycomb lattice, and propose and analyze a realistic scheme for analog quantum simulation of this model with cold atoms in a two-dimensional hexagonal optical lattice. To this end, we first derive the zero-temperature phase diagram of the interacting model within a mean-field theory treatment. We show that besides a semimetallic and a charge-density-wave ordered phase, the system exhibits a quantum anomalous Hall phase, which is generated dynamically, i.e., purely as a result of the repulsive fermionic interactions and in the absence of any external gauge fields. We establish the topological nature of this dynamically created Mott-insulating phase by the numerical calculation of a Chern number, and we study the possibility of coexistence of this phase with any of the other phases characterized by local order parameters. Based on the knowledge of the mean-field phase diagram, we then discuss in detail how the interacting Hamiltonian can be engineered effectively by state-of-the-art experimental techniques for laser dressing of cold fermionic ground-state atoms with electronically excited Rydberg states that exhibit strong dipolar interactions.

We develop finite-temperature theory for a trapped dipolar Bose gas including thermal-exchange interactions. Previous treatments neglected these difficult-to-compute terms. We present a methodology for numerically evaluating the thermal-exchange contributions, making use of cylindrical symmetry. We then investigate properties of the dipolar gas, including calculating the excitation spectrum over the full range of trap anisotropy. We evaluate the contributions due to thermal exchange noting that, under some regimes, these effects can be at least as significant as the direct interaction. We therefore provide guidance as to when these cumbersome terms can be neglected and when care should be exercised regarding their omission.

Photon-photon scattering predicted by quantum electrodynamics has not been experimentally confirmed in the optical frequency range. This is due to its extremely small cross section in this energy range. Since the cross section rapidly increases with photon energy, we propose measuring the photon-photon scattering cross section by upshifting optical lasers to the 100-eV to keV range using four relativistic mirror schemes and colliding them. In two of the schemes we find that although the number of scattering events is small with realistic laser parameters, measurement could be possible with an accumulation of a large number of laser shots. In the two other schemes a large number of scattering events is possible, however, the use of large future laser systems will be necessary.

An inhomogeneous anisotropic medium with specific structure geometry can apply the tunable spin-dependent geometrical phase to the light passing through the medium, and thus can be used to steer the spin-dependent splitting (SDS) of light. In this paper, we exemplify this inference by the $q$ plate, an inhomogeneous anisotropic medium. It is demonstrated that when a linearly polarized light beam normally passes through a $q$ plate, $k$-space SDS first occurs, and then the real-space SDS in the far-field focal plane of a converging lens is distinguishable. Interestingly, the SDS, described by the normalized Stokes parameter $S_3$ shows a multilobe and rotatable splitting pattern with rotational symmetry. Further, by tailoring the structure geometry of the $q$ plate and/or the incident polarization angle of light, the lobe number and the rotation angle both are tunable. Our result suggests that the $q$ plate can serve as a potential device for manipulating the photon spin states and enable applications such as in nano-optics and quantum information.

A well-known manifestation of quantum entanglement is that it may lead to correlations that are inexplicable within the framework of a locally causal theory—a fact that is demonstrated by the quantum violation of Bell inequalities. The precise relationship between quantum entanglement and the violation of Bell inequalities is, however, not well understood. While it is known that entanglement is necessary for such a violation, it is not clear whether all entangled states violate a Bell inequality, even in the scenario where one allows joint operations on multiple copies of the state and local filtering operations before the Bell experiment. In this paper we show that all entangled states, or more precisely, all not-fully-separable states of arbitrary Hilbert space dimension and arbitrary number of parties, violate a Bell inequality when combined with another state which on its own cannot violate the same Bell inequality. This result shows that quantum entanglement and quantum nonlocality are in some sense equivalent, thus giving an affirmative answer to the aforementioned open question. It follows from our result that two entangled states that are apparently useless in demonstrating quantum nonlocality via a specific Bell inequality can be combined to give a Bell violation of the same inequality. Explicit examples of such activation phenomenon are provided.

We propose solid-state gyroscopes based on ensembles of negatively charged nitrogen-vacancy (${\mathrm{NV}}^{-}$) centers in diamond. In one scheme, rotation of the NV${}^{-}$ symmetry axis will induce Berry phase shifts in the ${\mathrm{NV}}^{-}$ electronic ground-state coherences proportional to the solid angle subtended by the symmetry axis. We estimate a sensitivity in the range of $5\times {10}^{-3}$ $\mathrm{rad}{\mathrm{s}}^{-1}{\mathrm{Hz}}^{-1/2}$ in a 1-mm${}^3$ sensor volume using a simple Ramsey sequence. Incorporating dynamical decoupling to suppress dipolar relaxation may yield a sensitivity at the level of ${10}^{-5}$ $\mathrm{rad}{\mathrm{s}}^{-1}{\mathrm{Hz}}^{-1/2}$. With a modified Ramsey scheme, Berry phase shifts in the ${}^{14}\mathrm{N}$ hyperfine sublevels would be employed. The projected sensitivity is in the range of ${10}^{-5}$ $\mathrm{rad}{\mathrm{s}}^{-1}{\mathrm{Hz}}^{-1/2}$, however, the lower gyromagnetic ratio of ${}^{14}\mathrm{N}$ nuclei reduces the sensitivity to magnetic-field noise by several orders of magnitude. Reaching ${10}^{-5}$ $\mathrm{rad}{\mathrm{s}}^{-1}{\mathrm{Hz}}^{-1/2}$ would represent an order of magnitude improvement over other compact, solid-state gyroscope technologies.

The natural notion of almost perfect state transfer (APST) is examined. It is applied to the modeling of efficient quantum wires with the help of $XX$ spin chains. It is shown that APST occurs in mirror-symmetric systems, when the 1-excitation energies of the chains are linearly independent over rational numbers. This result is obtained as a corollary of the Kronecker theorem in Diophantine approximation. APST happens under much less restrictive conditions than perfect state transfer and moreover accommodates the unavoidable imperfections. Some examples are discussed.

We study the confidence and backaction of state reconstruction based on a continuous weak measurement and the quantum filter equation. As a physical example we use the traditional model of a double quantum dot being continuously monitored by a quantum point contact. We examine the confidence of the estimate of a state constructed from the measurement record, and the effect of backaction of that measurement on that state. Finally, in the case of general measurements we show that using the relative entropy as a measure of confidence allows us to define the lower bound on the confidence as a type of quantum discord.

Linear optics quantum computing (LOQC) is a leading candidate for the implementation of large scale quantum computers. Here quantum information is encoded into the quantum states of light and computation proceeds via a linear optics network. It is well known that in such schemes there are stringent requirements on the spatiotemporal structure of photons—they must be completely indistinguishable and of very high purity. We show that in the boson-sampling model for LOQC these conditions may be significantly relaxed. We present evidence that by increasing the size of the system we can implement a computationally hard algorithm even if our photons have arbitrarily low fidelity and purity. These relaxed conditions may make boson-sampling LOQC within reach of present-day technology.

We consider two entangled qubits, each of which is coupled to its own reservoir, so that their entanglement degrades with time. To enhance the qubits’ entanglement at a time during the evolution we propose a proper combination of pre- and postmeasurements to be performed locally on individual qubits. The premeasurements are weak measurements, but the postmeasurements may be either quantum measurement reversals or weak measurements again, depending on the situation at the time they are applied. Given the parameters of the initial qubits’ state, the premeasurements’ strength, and the evolution time, we establish the optimal conditions for the postmeasurements so that the qubits’ entanglement becomes the largest possible. Actually, by our scheme, less entangled qubits can evolve into more entangled ones with a finite probability, or even into a near-maximally entangled state but with a vanishingly low probability. We also examine the entanglement distribution among different pairs of subsystems involved and find out that the pairwise concurrence dynamics in our scheme differs strikingly from that in the situation without any control actions.