We investigate the classical nonrelativistic dynamics of three bodies in Efimov's $-1/R^2$ potential in three spatial dimensions, with a view towards semiclassical quantization and insight into the geometry of Efimov states. Without the short-distance cutoff, these dynamics are superintegrable, which allows an exact integration of the equations of motion for arbitrary initial conditions. We show that periodic orbits necessarily lead to exactly vanishing binding energy of the bound states, in disagreement with Efimov's quantum-mechanical results. A scaling anomaly demands that the quantum dynamics of three bodies in this potential be augmented by additional boundary conditions affecting all three particles at the short-distance cutoff point, i.e., near the triple collision. We discuss the inherent difficulties in the definition of appropriate three-body boundary conditions in three spatial dimensions and briefly discuss their consequences for (quasi)periodic orbits. Consequently, the classical orbits corresponding to Efimov states cannot be exactly periodic, but must have a finite timescale (lifetime), associated with the time it takes the system's hyperradius to fall to zero, or to the cutoff value, which is typically much longer than the (quasi)period of the hyperangular motion. The scaling properties of the lifetime are in agreement with the quantum-mechanical predictions of the half-life (width) of Efimov states surrounded by an ultracold gas. Detailed spatiotemporal evolution of the system is generally unpredictable beyond the three-body collision point, even though global conservation laws ensure that the system's hyperradius must be periodic.

The superfluid flow velocity is proportional to the gradient of the phase of the superfluid order parameter, leading to the quantization of circulation around a vortex core. In this work, we study the dynamics of a superfluid film on the surface of a torus. Such a compact surface allows only configurations of vortices with zero net vorticity. We derive analytic expressions for the flow field, the total energy, and the time-dependent dynamics of the vortex cores. The local curvature of the torus and the presence of noncontractable loops on this multiply connected surface alter both the superfluid flow and the vortex dynamics. Finally, we consider more general surfaces of revolution, called toroids.

In this work we study the single-qubit quantum state transfer in uniform long-range spin $XXZ$ systems in high-dimensional geometries. We consider prototypical long-range spin exchanges that are relevant for experiments in cold atomic platforms: Coulomb, dipolar, and van der Waals-like interactions. We find that in all these cases the fidelity increases with the dimensionality of the lattice. We also find a pronounced enhancement of the fidelity in one-dimensional lattices for increasing interaction range. This can be related to the emergence of a pair of bilocalized states on the sender and receiver site due to the onset of an effective weak-coupling Hamiltonian. Finally, we test our predictions in the presence of temperature-induced disorder introducing a model for the thermal displacement of the lattice sites, considered as a set of local adiabatic oscillators.

We find that a suppression of the collapse and revival of population inversion occurs in response to insertion of Gaussian quenched disorder in atom-cavity interaction strength in the Jaynes-Cummings model. The character of suppression can be significantly different in the presence of non-Gaussian disorder, which we uncover by studying the cases when the disorder is uniform, discrete, and Cauchy-Lorentz. Interestingly, the quenched averaged atom-photon entanglement keeps displaying nontrivial oscillations even after the population inversion has been suppressed. Subsequently, we show that disorder in atom-cavity interactions helps to avoid sudden death of atom-atom entanglement in the double Jaynes-Cummings model. We identify the minimal disorder strengths required to eliminate the possibility of sudden death. We also investigate the response of entanglement sudden death in the disordered double Jaynes-Cummings model in the presence of atom-atom coupling.

The evenly spaced modes of an electromagnetic resonator are coupled to each other by appropriate time modulation, leading to dynamics analogous to those of particles hopping between different sites of a lattice. This substitution of a real spatial dimension of a lattice with a “synthetic” dimension in frequency space greatly reduces the hardware complexity of an analog quantum simulator. Complex control and readout of a highly multimoded structure can thus be accomplished with very few physical control lines. We demonstrate this concept with microwave photons in a superconducting transmission line resonator by modulating the system parameters at frequencies near the resonator's free spectral range and observing propagation of photon wave packets in time domain. The linear propagation dynamics are equivalent to a tight-binding model, which we probe by measuring scattering parameters between frequency sites. We extract an approximate tight-binding dispersion relation for the synthetic lattice and initialize photon wave packets with well-defined quasimomenta and group velocities. As an example application of this platform in simulating a physical system, we demonstrate Bloch oscillations associated with a particle in a periodic potential and subject to a constant external field. The simulated field strongly affects the photon dynamics despite photons having zero charge. Our observation of photon dynamics along a synthetic frequency dimension generalizes immediately to topological photonics and single-photon power levels, and expands the range of physical systems addressable by quantum simulation.

In this work we investigate quantum-enhanced target detection in the presence of large background noise using multidimensional quantum correlations between photon pairs generated through spontaneous parametric down-conversion. Until now similar experiments have only utilized one of the photon pairs' many degrees of freedom such as temporal correlations and photon number correlations. Here, we utilized both temporal and spectral correlations of the photon pairs and achieved over an order of magnitude reduction to the background noise and in turn significant reduction to data acquisition time when compared to utilizing only temporal modes. We believe this work represents an important step in realizing a practical, real-time quantum-enhanced target detection system. The demonstrated technique will also be of importance in many other quantum sensing applications and quantum communications.

Many physical systems exhibit marginally unstable periodic orbits, which are nonhyperbolic families of periodic orbits appearing as segmented line structures with zero Lebesgue measure coexisting with hyperbolic components in phase space. Orbits in their vicinity escape in a subexponential manner which is in strong contrast to orbits near unstable periodic orbits which escape in an exponential way. By selectively exciting a series of modes in a rounded D-shape microdisk containing an InGaAsP multiquantum well, we experimentally demonstrate that marginally unstable periodic orbits can support a much more robust lasing than conventional unstable periodic orbits. Through numerical computations, we also compare quality factors of modes localized on marginally unstable periodic orbits and on stable periodic orbits.

We study conditions for the generation of strongly correlated photons of two extremely different frequency ranges, optical and terahertz, via the spontaneous parametric down-conversion effect in a nonlinear medium. Analytical expressions for the correlation function are derived using equations of the generalized Kirchhoff law for the second-order field moments with account of both classical thermal and quantum vacuum field fluctuations, possible inherent absorption of the medium at terahertz frequencies, and angular divergences of signal and idler radiation caused by a transverse limited spatial profile of the Gaussian pump beam. Associated with the current absence of terahertz photon counting detectors and coincidence schemes, the possible experimental limitations in measuring the second-order optical-terahertz field correlations are studied. Numerical calculations of noncollinear eee-geometry parametric down-conversion in a $\mathrm{Mg}:\mathrm{LiNb}{\mathrm{O}}_3$ crystal demonstrate angular characteristics, particular features of the temperature and spectral behavior of the second-order quantum correlation function of optical-terahertz biphotons.

We present a simple extension of the semiclassical model for a two-level system in a cavity, in order to incorporate multiple polarized transitions, such as those appearing in neutral and charged quantum dots (QDs), and two nondegenerate linearly polarized cavity modes. We verify the model by exact quantum master equation calculations and experimentally using a neutral QD in a polarization nondegenerate microcavity, and in both cases we observe excellent agreement. Finally, the usefulness of this approach is demonstrated by optimizing a single-photon source based on polarization postselection, where we find an increase in the brightness for optimal polarization conditions as predicted by the model.

We explore amplification and cross-Kerr nonlinearity by a three-level emitter (3LE) embedded in a waveguide and driven by two light beams. The coherent amplification and cross-Kerr nonlinearity were demonstrated in recent experiments, respectively, with a $\mathsf{V}$ and a ladder-type 3LE coupled to an open superconducting transmission line carrying two microwave fields. Here, we consider $\mathrm{\Lambda },\mathsf{V}$, and ladder-type 3LE, and compare the efficiency of coherent and incoherent amplification as well as the magnitude of the cross-Kerr phase shift in all three emitters. We apply the Heisenberg-Langevin equations approach to investigate the scattering of a probe and a drive beam, both initially in coherent states. We particularly calculate the regime of the probe and drive powers when the 3LE acts most efficiently as a coherent amplifier and derive the second-order coherence of amplified probe photons. Finally, we apply the Kramers-Kronig relations to correlate the amplitude and phase response of the probe beam, which are used in finding the coherent amplification and the cross-Kerr phase shift in these systems.

Based on the concepts of quantum synchronization and quantum phase synchronization proposed by A. Mari et al. [Phys. Rev. Lett. 111, 103605 (2013)], we introduce and characterize the measure of a more generalized quantum synchronization called quantum $\varphi$ synchronization under which pairs of variables have the same amplitude and possess the same $\varphi$ phase shift. Naturally, quantum synchronization and quantum antisynchronization become special cases of quantum $\varphi$ synchronization. Their relations and differences are also discussed. To illustrate these theories, we investigate the quantum $\varphi$ synchronization and quantum phase synchronization phenomena of two coupled optomechanical systems with periodic modulation and show that quantum $\varphi$ synchronization is more general as a measure of synchronization. We also show the phenomenon of quantum antisynchronization when $\varphi =\pi$.

Quantum network coding has been proposed to improve resource utilization to support distributed computation but has not yet been put into practice. We investigate a particular implementation of quantum network coding using measurement-based quantum computation on IBM Q processors. We compare the performance of quantum network coding with entanglement swapping and entanglement distribution via linear cluster states. These protocols outperform quantum network coding in terms of the final Bell pair fidelities but are unsuitable for optimal resource utilization in complex networks with contention present. We demonstrate the suitability of noisy intermediate-scale quantum devices such as the IBM Q for the study of quantum networks. We also identify the factors that limit the performance of quantum network coding on these processors and provide estimates of error rates required to boost the final Bell pair fidelities to a point where they can be used for generation of genuinely random cryptographic keys, among other useful tasks. Surprisingly, the required error rates are only around a factor of 2 smaller than the current status, and we expect they will be achieved in the near future.

High-fidelity manipulation is key to the physical realization of fault-tolerant quantum computation. Here, we present a protocol to realize universal nonadiabatic geometric gates for silicon-based spin qubits. We find that the advantage of geometric gates over dynamical gates depends crucially on the evolution loop for the construction of the geometric phase. Under appropriate evolution loops, all geometric single- and two-qubit gates can outperform their dynamical counterparts for both systematic and off-resonance noises. We also perform randomized benchmarking using noise amplitudes consistent with experiments in silicon. For the static noise model, the averaged fidelities of geometric gates are around 99.90% or above, while for the time-dependent $1/f$-type noise, the fidelities are around 99.98% when only the off-resonance noise is present. We also show that the improvement in fidelities of the geometric gates over dynamical ones typically increases with the exponent $\alpha$ of the $1/f$ noise, and the ratio can be as high as 4 when $\alpha \approx 3$. Our results suggest that geometric gates with judiciously chosen evolution loops can be a powerful way to realize high-fidelity quantum gates.

We theoretically analyze the performance of the nuclear magnetic resonance (NMR) spectroscopy with a superconducting flux qubit (FQ). Such NMR with the FQ is attractive because of the possibility to detect the relatively small number of nuclear spins in a local region ($\approx \mu \mathrm{m}$) with low temperatures ($\approx \mathrm{mK}$) and low magnetic fields ($\approx \mathrm{mT}$), in which other types of quantum sensing schemes cannot easily be accessed. A sample containing nuclear spins is directly attached on the FQ, and the FQ is used as a magnetometer to detect magnetic fields from the nuclear spins. Especially, we consider two types of approaches to NMR with the FQ. One of them is to use spatially inhomogeneous excitations of the nuclear spins, which are induced by a spatially asymmetric driving with radio-frequency (rf) pulses. Such an inhomogeneity causes a change in the dc magnetic flux penetrating a loop of the FQ, which can be detected by a standard Ramsey measurement on the FQ. The other approach is to use a dynamical decoupling on the FQ to measure ac magnetic fields induced by Larmor precession of the nuclear spins. In this case, neither a spin excitation nor a spin polarization is required since the signal comes from fluctuating magnetic fields of the nuclear spins. We calculate the minimum detectable density (number) of the nuclear spins for the FQ with experimentally feasible parameters. We show that the minimum detectable density (number) of the nuclear spins with these approaches is around ${10}^{21}/{\mathrm{cm}}^3$ (${10}^8$) with an accumulation time of 1 s.

Experimentalists use particles as tracers in liquid helium. The intrusive effects of particles on the dynamics of vortices remain poorly understood. We implement a study of how basic, well understood vortex states, such as a propagating pair of oppositely signed vortices, change in the presence of particles by using a simple model based on the Magnus force. We focus on the two-dimensional case, and compare the analytic and semianalytic models with simulations of the Gross-Pitaevskii (GP) equation with particles modeled by dynamic external potentials. The results confirm that the Magnus force model is an effective way to approximate vortex-particle motion either with closed-form simplified solutions or with a more accurate numerically solvable ordinary differential equations. Furthermore, we increase the complexity of the vortex states and show that the suggested semianalytical model remains robust in capturing the dynamics observed in the GP simulations.

We study a system of $N$ noninteracting spinless fermions in a confining double-well potential in one dimension. We show that when the Fermi energy is close to the value of the potential at its local maximum, physical properties, such as the average density and the fermion position correlation functions, display a universal behavior that depends only on the local properties of the potential near its maximum. This behavior describes the merging of two Fermi gases, which are disjoint at sufficiently low Fermi energies. We describe this behavior in terms of a correlation kernel that we compute analytically and we call it the inverted parabola kernel. As an application, we calculate the mean and variance of the number of particles in an interval of size $2L$ centered around the position of the local maximum, for sufficiently small $L$. We discuss the possibility of observing our results in experiments, as well as extensions to nonzero temperature and to higher space dimensions.

The traditional method for measuring Einstein-Podolsky-Rosen-type continuous-variable quantum entanglement relies on balanced homodyne detections, which are sensitive to vacuum quantum noise coupled in through losses due to various factors such as detector quantum efficiency and mode mismatching between the detected field and the local oscillator. In this paper, we propose and analyze a measurement method, which is realized by assisting the balanced homodyne detections with a high-gain phase-sensitive parametric amplifier. The employment of the phase-sensitive amplifier helps us to tackle the vacuum quantum noise originating from detection losses. Moreover, because the high-gain phase-sensitive amplifier can couple two fields of different types, the proposed scheme can be used to reveal quantum entanglement between two fields of different types by using only one balanced homodyne detection. Furthermore, detailed analysis shows that in the multimode case, the proposed scheme is also advantageous over the traditional method. Such a measurement method should find wide applications in quantum information and quantum metrology involving measurement of continuous variables.

Photon blockade via a giant self-Kerr nonlinearity in an optical resonator induced by an N-type quantum system is one of the main routines towards photon-based quantum information processing. However, such an N-type system for phonons is lacking. We propose an effective N-type quantum system for phonons, forming from a superconducting transmon qubit and a microwave resonator. In the absence of any external driving, the quantum vacuum-qubit interaction causes the surface acoustic wave (SAW) phonon blockade. Such a vacuum-induced phonon blockade paves the way to prepare single SAW phonons from a weak coherent phononic state for SAW accessible superconducting quantum computation.

Various quantum phase transitions in the anisotropic Rabi-Stark model with both the nonlinear Stark coupling and the linear dipole coupling between a two-level system and a single-mode cavity are studied in this work. The first-order quantum phase transitions are detected by the level crossing of the ground-state and the first-excited state with the help of the pole structure of the transcendental functions derived by the Bogoliubov operators approach. As the nonlinear Stark coupling is the same as the cavity frequency, this model can be solved by mapping to an effective quantum oscillator. All energy levels close at the critical coupling in this case, indicating continuous quantum phase transitions. The critical gap exponent is independent of the anisotropy as long as the counter-rotating wave coupling is present, but essentially changed if the counter-rotating wave coupling disappears completely. It is suggested that the gapless Goldstone mode excitations could appear above a critical coupling in the present model in the rotating-wave approximation.

The evolution of a quantum system towards thermal equilibrium is usually studied by approximate methods, which have their limits of validity and should be checked against analytically solvable models. In this paper, we propose an analytically solvable model to investigate the energy transfer between a bosonic bath and a fermionic chain which are nonlinearly coupled to each other. The bosonic bath consists of an infinite collection of noninteracting bosonic modes, while the fermionic chain is represented by a chain of interacting fermions with nearest-neighbor interactions. We compare the behaviors of the temperature-dependent energy current $J_T$ and temperature-independent energy current $J_{TI}$ for different bath configurations. With respect to the bath spectrum, $J_T$ decays exponentially for a Lorentz-Drude-type bath, which is the same as the conventional approximations. On the other hand, the decay rate is $1/t^3$ for the Ohmic type and $1/t$ for white noise, which does not have conventional counterparts. For the temperature-independent current $J_{TI}$, the decay rate is divergent for the Lorentz-Drude-type bath, $1/t^4$ for the Ohmic bath, and $1/t$ for the white noise. When further considering the dynamics of the fermionic chain, the current will be modulated based on the envelope from the bath. As an example, for a bosonic bath with an Ohmic spectrum, when the fermionic chain is uniformly coupled, we have $J_T\propto 1/t^6$ and $J_{TI}\propto 1/t^3$. Moreover, it is interesting that $J_T$ is proportional to ${(N-1)}^{1/2}$ at certain times for perfect state transfer couplings under a Lorentz-Drude or Ohmic bath.