As the Earth rotates, the Coriolis force causes various oceanic and atmospheric waves to be trapped along the equator, including Kelvin, Yanai, Rossby, and Poincaré modes. It has been demonstrated that the mathematical origin of these waves is related to the nontrivial topology of the underlying hydrodynamic equations. Inspired by recent observations of Bose-Einstein condensation (BEC) in bubble-shaped traps in microgravity ultracold quantum gas experiments, we demonstrate that equatorial modes are supported by a rapidly rotating condensate in a spherical geometry. Using a zero-temperature coarse-grained hydrodynamic framework, we reformulate the coupled oscillations of the superfluid and the Abrikosov vortex lattice resulting from rotation as a Schrödinger-like eigenvalue problem. The resulting non-Hermitian Hamiltonian is topologically nontrivial. We also solve the hydrodynamic equations for a spherical geometry and find that the rotating superfluid hosts Kelvin, Yanai, and Poincaré equatorial modes, but not the Rossby mode. Our predictions can be tested with state-of-the-art bubble-shaped trapped BEC experiments.

We address the existence and dynamics of one-dimensional harmonically confined quantum droplets appearing in two-component mixtures by deploying a nonperturbative approach. We find that, in symmetric homonuclear settings, beyond-Lee-Huang-Yang correlations result in flat-top droplet configurations for either decreasing intercomponent attraction or larger atom number. Asymmetric mixtures feature spatial mixing among the involved components with the more strongly interacting or heavier one exhibiting flat-top structures. Applying quenches on the harmonic trap we trigger the lowest-lying collective droplet excitations. The interaction-dependent breathing frequency, being slightly reduced in the presence of correlations, shows a decreasing trend for stronger attractions. Semianalytical predictions are also obtained within the Lee-Huang-Yang framework. For relatively large quench amplitudes the droplet progressively delocalizes and higher-lying motional excitations develop in its core. Simultaneously, enhanced intercomponent entanglement and long-range two-body intracomponent correlations arise. In sharp contrast, the dipole motion remains robust irrespective of the system parameters. Species-selective quenches lead to a correlation-induced dephasing of the droplet or to irregular dipole patterns due to intercomponent collisions.

Experimental evidence of the Higgs mode in strongly interacting superfluid Fermi gases had not been observed until recently [Behrle et al., Nat. Phys. 14, 781 (2018).]. Due to the coupling with other collective modes and quasiparticle excitations, generating stable Higgs-mode oscillations is challenging. We study how to excite long-lived Higgs-mode oscillations in a homogeneous superfluid Fermi gas in the BCS-BEC crossover. We find that the Higgs mode can be excited by time-periodically modulating the scattering length at an appropriate amplitude and frequency. However, even for a modulation frequency below twice the pairing-gap energy, quasiparticles are still excited through the generation of higher harmonics due to nonlinearity in the superfluid. More importantly, we find that persistent Higgs-mode oscillations with almost constant amplitude can be produced by removing particles at an appropriate momentum, and the oscillation amplitude can be controlled by the number of removed particles. Finally, we propose two ways to experimentally realize particle removal.

The Kochen-Specker theorem states that exclusive and complete deterministic outcome assignments are impossible for certain sets of measurements, called Kochen-Specker (KS) sets. A straightforward consequence is that KS sets do not have joint probability distributions because no set of joint outcomes over such a distribution can be constructed. However, we show it is possible to construct a joint quasiprobability distribution over any KS set by relaxing the completeness assumption. Interestingly, completeness is still observable at the level of measurable marginal probability distributions. This suggests the observable completeness might not be a fundamental feature, but a secondary property.

A single bichromatic field near resonant to a qubit transition is typically used for ${\widehat{\sigma }}_x$ or ${\widehat{\sigma }}_y$ Mølmer-Sørensen-type interactions in trapped-ion systems. Using this field configuration, it is also possible to synthesize a ${\widehat{\sigma }}_z$ spin-dependent force by merely adjusting the beat-note frequency. Here, we expand on previous work and present a comprehensive theoretical and experimental investigation of this scheme with a laser near resonant to a quadrupole transition in ${}^{88}\mathrm{Sr}^{+}$. Further, we characterize its robustness to optical phase and qubit frequency offsets, and demonstrate its versatility by entangling optical, metastable, and ground-state qubits.

Single-atom high-order harmonic generation (HHG) induced by an intense linearly polarized infrared (IR) field and assisted by a perturbative extreme ultraviolet (XUV) short pulse with linear polarization is analyzed in perpendicular geometry. It is shown that for the case of the initial $p$ state, the two independent projections of the laser-induced dipole are formed by two independent physical channels, which are responsible for IR-induced HHG and XUV-initiated HHG. This property of the laser-induced dipole is utilized for polarization control of the generated radiation. An alternative scheme for studying XUV-initiated HHG is proposed.

Spin-1 spin-orbit-coupled spinor Bose-Einstein condensates have been realized in experiment. We study spin-orbit-coupled spinor gap solitons in this experimentally realizable system with an optical lattice. The spin-dependent parity symmetry of the spin-orbit coupling plays an important role in the properties of gap solitons. Two families of solitons with opposite spin-dependent parity are found. Using an approximate model by replacing the optical lattice with a harmonic trap, we demonstrate the physical origin of the two families. For the zero effective quadratic Zeeman shift, we also find a type of gap soliton that spontaneously breaks the spin-dependent parity symmetry.

The scattering properties of spin-polarized Fermi gases are dominated by $p$-wave interactions. Besides their inherent angular dependence, these interactions differ from their $s$-wave counterparts as they also require the presence of a finite effective range in order to understand the low-energy properties of the system. In this article we examine how the shear viscosity and thermal conductivity of a three-dimensional spin-polarized Fermi gas in the normal phase depend on the effective range and the scattering volume in both the weakly and the strongly interacting limits. We show that, although the shear viscosity and the thermal conductivity both explicitly depend on the effective range near resonance, the Prandtl number which parametrizes the ratio of momentum to thermal diffusivity does not have an explicit interaction dependence both at resonance and for weak interactions in the low-energy limit. In contrast to $s$-wave systems, $p$-wave scattering exhibits an additional resonance at weak attraction from a quasi-bound state at positive energies, which leads to a pronounced dip in the shear viscosity at specific temperatures.

The exact expressions of finesse and full width at half maximum (FWHM) of the Airy distribution of a Fabry-Pérot (FP) resonator are derived, which solves the breakdown problem at ultralow reflectivity in traditional formulas. We demonstrate that, when the cavity-mirror reflectivity $R\to 0$, the FWHM approaches half of the free spectral range rather than infinity; moreover, the cavity finesse $\mathcal{F}$ approaches 2 rather than zero. These expressions are useful for the development of bad-cavity lasers, such as the four-level active optical clock based on the strong atomic transition of cesium. Also, the exact expressions of the FWHM and finesse of the reflection distribution composed of reflected mode profiles are derived, which separately intersect with that of the Airy one at $R=0$. In addition, the characteristics of an antiresonant cavity, the frequency of which is exactly at the center of two adjacent resonant cavity modes, are analyzed. It is demonstrated that at the resonant and antiresonant frequencies the enhancement and inhibition of intracavity light intensity caused by the FP cavity are symmetrical in the logarithmic view. Furthermore, we provide a universal expression of the cavity-enhancement factor rather than the classical representation of “$\text{2}\mathcal{F}/\phantom{\text{2}\mathcal{F}\pi }\pi$,” which is inadequate for the high-loss cavity because the cavity-enhancement factor should naturally reach 1 when $R\to 0$. Finally, we extend the application of the antiresonant cavity to an inhibited laser, the frequency of which has a stronger suppression effect on the cavity-length thermal noise than the traditional resonant laser.

A method of analysis for a randomly scattering analyzer offering far-subwavelength spatial resolution with coherent light is presented, and the attributes are supported by numerical simulations. Without constraints, far-field detection generally results in a spatial resolution of about one wavelength, mathematically explained through the loss of the evanescent field information in a plane-wave expansion. Enhanced spatial resolution is shown to be possible because of relative motion with a structured field and the resulting information available. It is shown that detected information through a scattering analyzer results in enhanced spatial sensitivity with motion of an object in a structured field, and that this is accompanied by changes in the relative distribution of significant eigenvalues of the transmission matrix modeling the analyzer. Thus, the character of the random analyzer is shown to influence the far-field spatial resolution. A random analyzer, in principle, allows subwavelength sensitivity whose resolution is limited only by measurement accuracy and precision, when fields are scattered from a moving object or when some other relative change causes a modified field. Consequently, use of a random analyzer offers substantial impact in a variety of applications.

The dynamical control of single-photon scattering in a one-dimensional waveguide coupled to a Floquet atom-cavity system with time-modulated coupling constants is investigated. The analytical expressions for determining the scattering properties are obtained by using an effective Floquet Hamiltonian in real space. The photon transport is extremely sensitive to the time-modulated atom-cavity coupling strengths. Two cases, i.e., the effective Floquet Hamiltonian either includes or excludes a static coupling term, are discussed in detail. The results show that, with such Floquet atom-cavity configuration, an active photonic switch with nearly ideal switching contrast could be implemented. The transmission of the waveguide photons with different frequencies can dynamically be switched on or off via adjusting the modulated amplitude or relative modulated phase no matter whether the static coupling between the atom and the two cavity modes is considered or not. The application of the dynamic modulated atom-cavity coupling strengths instead of a purely static one makes our photonic switch more tunable. These results are expected to be applicable in quantum information processing and in active quantum device design involving dynamical modulation.

Analytic expression is found for the frequency dependence of the transmission coefficient of a transmission line inductively coupled to the microwave cavity with the superradiant condensate. Sharp transmission drops reflect the condensate's frequencies spectrum. These results pave the way to direct detection of emergence of the superradiant condensates in quantum metamaterials. Results are based on the analytic solutions of the nonlinear semiclassical dynamics of the superradiant photonic condensate in the Dicke model of an ensemble of two-level atoms dipolar coupled to the electromagnetic field in the microwave cavity. In the adiabatic limit with respect to the photon degree of freedom, the system is approximately integrable with evolution being expressed via Jacobi elliptic functions of real time. Depending on the coupling strength, the semiclassical coordinate of the superradiant condensate in the ground state either oscillates in one of the two degenerate minima of the condensate's potential energy or traverses between them over the saddle point. An experimental setup for measuring of the breakdown of the normal phase of the Dicke model via coupling to the transmission line is proposed. A one-to-one mapping of the semiclassical motion of the superradiant condensate on the nodding of unstable Lagrange “sleeping top” also turns the Dicke model into an analog device for modeling the dynamics of mechanical systems.

We describe a quantum dynamo effect in a driven system coupled to a harmonic oscillator describing a cavity mode or to a collection of modes forming an Ohmic bosonic bath. When the system Hamiltonian changes in time, this induces a dynamical field in the bosonic modes having resonant frequencies with the driving velocity. This field opposes the change of the external driving field in a way reminiscent of Faraday's law of induction, justifying the term “quantum dynamo effect.” For the specific situation of a periodically driven spin-$\frac{1}{2}$ on the Bloch sphere, we show that the work done by rolling the spin from the north to south pole can efficiently be converted into a coherent displacement of the resonant bosonic modes, and the effect thus corresponds to a work-to-work conversion and allows us to interpret this transmitted energy into the bath as work. We study this effect, its performance, and limitations in detail for a driven spin-$\frac{1}{2}$ in the presence of a radial magnetic field addressing a relation with topological systems through the formation of an effective charge in the core of the sphere. We show that the dynamo effect is directly related to the dynamically measured topology of this spin-$\frac{1}{2}$ and thus in the adiabatic limit provides a topologically protected method to convert driving work into a coherent field in the reservoir. The quantum dynamo model is realizable in mesoscopic and atomic systems.

A steady current between baths is a manifestation of the prethermalization phenomenon, a quasiequilibrium dynamic process with weak breaking of conserved quantities. We consider two finite nonintegrable many-body baths, each following the eigenstate thermalization hypothesis and each prepared in a random product state with fixed and different energy constraints, i.e., within the mean energy ensemble. Such an initialization, not being constrained to superpositions or mixtures of many-body eigenstates, opens the door to experimental realization and also significantly simplifies numerical simulations. We show that such a dynamic process is typical as the current variance decreases exponentially with respect to the size of baths. We also demonstrate that the emerging current is prethermalized in a strong sense, analogous to strong thermalization, meaning that the current values stay close to the microcanonical one most of the time.

We study the quantum phase synchronization of a driven two-level system (TLS) coupled to a structured environment and demonstrate that quantum synchronization can be enhanced by the classical driving field. We use the Husimi $Q$ function to characterize the phase preference and find the in-phase and anti-phase locking phenomenon in the phase diagram. Remarkably, we show that the in-phase classical driving enables a TLS to reach stable anti-phase locking in the Markovian regime. However, we find that the synergistic action of classical driving and non-Markovian effects significantly enhances the initial in-phase locking. By introducing the $S$ function and its maximal value to quantify the strength of synchronization and sketch the synchronization regions, we observe the typical signatures of the hollowed Arnold tongue in the parameter regions of synchronization. In the hollowed Arnold tongue, the synchronization regions exist both inside and outside the tongue while unsynchronized regions only lie on the boundary line. We also provide an intuitive interpretation of the above results by using the quasimode theory.

We pay attention to the influences of the nonreciprocal coupling on the band structures and skin effects in the coupled Su-Schrieffer-Heeger (SSH) lattices. It is shown that the nonreciprocal coupling leads to the non-Hermitian skin effect in a substantial way. Besides, it widens the parameter space of the zero-energy modes in the band gap, and modifies the transition manner from the topologically trivial to topologically nontrivial phase. When the nonreciprocal coupling exceeds its critical value, the zero-energy modes will split, giving rise to the appearance of new nonzero- or complex-energy modes. What is more, differently from the chain configuration, the nonreciprocal coupling makes purely imaginary energy modes emerge in the band gap of the SSH-ring configuration. Next in the presence of hopping disorder, we observe that the zero-energy modes are relatively robust, whereas the imaginary part of energies displays the nonmonotonic changes. It can be thus believed that all these findings promote understanding the influences of nonreciprocal couplings on the types and properties of isolated modes in the SSH lattices.