It is well known that the topological entanglement entropy ($S_{\mathrm{topo}}$) of a topologically ordered ground state in two spatial dimensions can be captured efficiently by measuring the tripartite quantum information ($I^3$) of a specific annular arrangement of three subsystems. However, the nature of the general $N$-partite information ($I^N$) and correlation of a topologically ordered ground state remains unknown. In this work, we study such $I^N$ measure and its nontrivial dependence on the arrangement of $N$ subsystems. For the collection of subsystems (CSS) forming a closed annular structure, the $I^N$ measure ($N\ge 3$) is a topological invariant equal to the product of $S_{\mathrm{topo}}$ and the Euler characteristic of the CSS embedded on a planar manifold, $|I^N|=\chi S_{\mathrm{topo}}$. Importantly, we establish that $I^N$ is robust against several deformations of the annular CSS, such as the addition of holes within individual subsystems and handles between nearest-neighbor subsystems. While the addition of a handle between further neighbor subsystems causes $I^N$ to vanish, the multipartite information measures of the two smaller annular CSS emergent from this deformation again yield the same topological invariant. For a general CSS with multiple holes ($n_h>1$), we find that the sum of the distinct, multipartite information measured on the annular CSS around those holes is given by the product of $S_{\mathrm{topo}}, \chi$ and $n_h, {\sum }_{{\mu }_i=1}^{n_h}\left|I_{{\mu }_i}^{N_{{\mu }_i}}\right|=n_h\chi S_{\mathrm{topo}}$. This constrains the concomitant measurement of several multipartite information on any complicated CSS. The $N\text{th}$ order irreducible correlations for an annular CSS of $N$ subsystems is also found to be bounded from above by $|I^N|$, which shows the presence of correlations among subsystems arranged in the form of closed loops of all sizes. Thus, our results offer important insight into the nature of the many-particle entanglement and correlations within a topologically ordered state of matter.

We present a second quantization description of frequency-based continuous variables quantum computation in the subspace of single photons. For this, we define frequency and time operators using the free-field Hamiltonian and its Fourier transform, and we show that these observables, when restricted to the one photon per mode subspace, reproduce the canonical position-momentum commutation relations. As a consequence, frequency and time operators can be used to define a universal set of gates in this particular subspace. We discuss the physical implementation of these gates as well as their effect on single photon states, and show that frequency and time variables can also be used to implement continuous variables quantum information protocols, in the same way than polarization is currently used as a two-dimensional quantum variable.

Improving the clock stability is of fundamental importance for the development of quantum-enhanced metrology. One of the main limitations arises from the randomly fluctuating local oscillator (LO) frequency, which introduces “phase slips” for long interrogation times and hence the failure of the frequency-feedback loop. Here we propose a strategy to improve the stability of atomic clocks by interrogating two atomic ensembles sharing the same LO. The two ensembles are prepared in coherent spin states pointing along orthogonal directions in the Bloch sphere. While standard Ramsey interrogation can only determine phases unambiguously in the interval $[-\pi /2,\pi /2]$, the joint interrogation allows for an extension to $[-\pi ,\pi ]$, resulting in a relaxed restriction of the Ramsey time and improvement of absolute clock stability. Theoretical predictions are supported by ab initio numerical simulation for white and correlated LO noise. While our basic protocol uses uncorrelated atoms, we further extended it to include spin-squeezing and further improving the scaling of clock stability with the number of atoms. Our protocol can be readily tested in current state-of-the-art experiments.

We study the effects of a position-dependent artificial gauge field on an atomic Bose-Einstein condensate in quasi-one-dimensional and two-dimensional ring settings. The inhomogeneous artificial gauge field can induce global and local currents in the Bose-Einstein condensate via phase gradients along the ring and vortices, respectively. We observe two different regimes in the system depending on the radial size of the ring and the strength of the gauge field. For weak artificial gauge fields, the angular momentum increases, as expected, in a quantized manner; however, for stronger values of the fields, the angular momentum exhibits a linear (nonquantized) behavior. We also characterize the angular momentum for noncylindrically symmetric traps.

Quantum interference, responsible for a number of resonant optical phenomena, always intrigues researchers because of its application in optical devices. This work studies it in multiwaveguide systems bridged by Jaynes-Cummings emitters (JCEs) based on the scattering matrix theory. Two types of quantum interference are distinguished here. The first is between the incident wave and those scattered from the JCEs, while the second is only among those scattered waves. The first type leads to the two transmission valleys at the two eigenfrequencies of the JCEs in single-waveguide–single-JCE coupled systems. However, the second type is responsible for the narrow transmission peaks in single-waveguide–multi-JCE coupled systems, locating in the above transmission valleys. This work first shows the properties of the second type of quantum interference in detail and then discusses its two applications. On the one hand, the second type of quantum interference can be used to tailor the transmission spectra to achieve the electromagnetically-induced-transparency-like line shapes with a large group delay. On the other hand, it can also lead to the single-photon jumping between two certain waveguides with a nearly $100\%$ chance in multiwaveguide systems by switching on or off some of the couplings of the JCEs to the waveguides. These applications with small peak widths commonly require a small loss and might have potential in quantum informatics.

Nonlinear Heisenberg-Langevin equations are solved analytically by operator Fourier expansion for the laser in the light-emitting diode (LED) regime. Fluctuations of populations of lasing levels are taken into account as perturbations. The spectra of operator products are calculated as convolutions, preserving Bose commutations for the lasing field operators. It is found that fluctuations of population significantly affect spontaneous and stimulated emissions into the lasing mode, increase the radiation rate, the number of lasing photons, and broaden the spectrum of a bad cavity threshold-less and the superradiant lasers. The method can be applied to various resonant systems in quantum optics.

We study theoretically laser excitation of Rydberg triplet states of strontium atoms in the presence of weak microwave (MW) fields. Starting from the ground state $5s^2{}^1{S}_0$, the Rydberg excitation is realized through the metastable, triplet $5s5p^3{P}_1$ state, whose decay rate ${\gamma }_2$ is $2\pi \times 7.5$ kHz, much smaller than the one in the singlet state or alkali-metal atoms. The influences of ${\gamma }_2$ on the transparency and absorption spectrum in the electromagnetically induced transparency (EIT), and electromagnetically induced absorption (EIA) regime are examined. Narrow transparent windows (EIT) or absorption peaks (EIA) are found, whose distance in the spectrum depends on the Rabi frequency of the weak MW field. It is found that the spectrum exhibits higher contrast than using the singlet state or alkali-metal atoms in typical situations. Using the metastable intermediate state, we find that the resonance fluorescence of Sr gases exhibits very narrow peaks, which are modulated by the MW field. When the MW field is weaker than the probe and control light, the spectrum distance of these peaks is linearly proportional to ${\mathrm{\Omega }}_m$. This allows us to propose an alternative way to sense very weak MW fields through resonance fluorescence. Our study shows that the Sr triplet state could be used to develop the Rydberg MW electrometry that gains unique advantages.

This paper proposes a generalized Bell-like inequality (GBI) for multiparticle entangled Schrödinger cat states of arbitrary spin $s$. Based on quantum probability statistics, the GBI and violation are formulated in a unified manner with the help of a state density operator, which can be separated into local and nonlocal parts. The local part gives rise to the inequality, while the nonlocal part is responsible for the violation. The GBI is not violated at all by the quantum average, except the spin-$1/2$ entangled states. If the measuring outcomes are restricted in the subspace of the spin coherent state (SCS), namely, only the maximum spin values $\pm s$, the GBI is still meaningful for the incomplete measurement. With the help of SCS quantum probability statistics, it is proved that the violation of GBI can occur only for half-integer spins and not integer spins. Moreover, the maximum violation bound depends on the number parity of the entangled particles, which is $1/2$ for the odd particle numbers and 1 for the even numbers.

We construct an $\mathrm{SU}\left(N\right)$ toric code model describing the dynamics of $\mathrm{SU}\left(N\right)$ electric and magnetic fluxes on a two-dimensional torus. We show that the model has $N^2$ topologically distinct ground states $|{\psi }_0{\rangle }_{(\mathsf{p},\mathsf{q})}$, which are the loop states characterized by $Z_N\otimes Z_N$ center charges $(\mathsf{p},\mathsf{q}=0,1,2,...,N-1)$. We explicitly construct them in terms of coherent superpositions of all possible spin network states on a torus with Wigner coefficients as their amplitudes. All excited quasiparticle states with $\mathrm{SU}\left(N\right)$ electric charges and magnetic fluxes are constructed. We show that the braiding statistics of these $\mathrm{SU}\left(N\right)$ electric or magnetic quasiparticles or non-Abelian anyons are encoded in the Wigner rotation matrices.

The matrix product state has been demonstrated to be able to explore the most relevant portion of the exponentially large quantum Hilbert space and find accurate solutions for one-dimensional interacting quantum many-body systems. Inspired by this success, here we propose a clustering algorithm based on the matrix product state, which first maps the classical data into quantum states represented as matrix product states, and then minimizes the loss function using a variational matrix product states algorithm in the enlarged space. We demonstrate this algorithm by applying it to several commonly used machine learning data sets, showing that this algorithm could reach higher learning precision and that it is less likely to be trapped in local minima compared to the standard K-means algorithm. We also show that this algorithm can achieve state-of-the-art learning precision on popular computer vision data sets when used in combination with better initialization schemes.

It is recognized that Grover arrived at his original quantum search algorithm inspired by his comprehension of the interference of classical waves originating from an array of antennas. It is also known that quantum-mechanical characterization of electromagnetic radiation is isomorphic to the treatment of the orientation of a spin-$1/2$ particle. In this paper, motivated by Grover's original intuition and starting from this mathematical equivalence, we present a quantitative link between the geometry of time-independent optimal-speed Hamiltonian evolutions on the Bloch sphere and the geometry of intensity-preserving propagation of light with maximal degree of coherence on the Poincaré sphere. Finally, identifying interference as the fundamental physical ingredient underlying both physical phenomena, we propose that our work can provide in retrospect a quantitative geometric background underlying Grover's powerful intuition.

The optical theorem is a fundamental aspect of quantum scattering theory. Here, we generalize this theorem to the case where the incident scattering state is a superposition of internal states of the collision partners, introducing additional interference contributions and, e.g., providing a route to control the total integral cross section. As in its standard form, forward scattering plays an essential role in the multichannel optical theorem, but with interference terms being related to the inelastic forward scattering amplitudes between states in the initial superposition. Using the resultant control index, we show that extensive control is possible over ultracold collisions of oxygen molecules in their rovibrational ground states, and of ${}^{85}\mathrm{Rb}\text{−}{}^{85}\mathrm{Rb}$ collisions, promising systems for the experimental demonstration of the quantum interference control of the total scattering cross section.

In this paper we study the nonlinearities present in a nano-optomechanical system consisting of a cantilever coupled to a racetrack resonator. We show that higher-order harmonics in the mechanical frequency spectrum are indicative of a readout nonlinearity and we connect these harmonics to the optical cavity transmission with detuning function and its derivatives. We also show that there are optical force nonlinearities that cause a Duffing-type response in the driven mechanical signal. The Duffing-type nonlinearity produces a nonlinear softening when the probe laser is blue detuned, and a nonlinear stiffening when the probe laser is red detuned. The optical force and readout nonlinearities are difficult to separate using a purely experimental approach. We demonstrate the use of a numerical model of the pump-and-probe system to analyze the nonlinearities independently. The numerical model also allows us to estimate the amplitude of the system, predicting the exact detuning where nonlinearities cancel each other to produce higher critical amplitude, and ultimately gives a prospective mass sensitivity level of $83\mathrm{yg}/{\mathrm{Hz}}^{1/2}$. The numerical model provides a rich understanding of the complexities of the nano-optomechanical system and is much needed for the development of sensors with increased dynamic range and overall performance.

According to von Neumann, the global Hamiltonian of the whole universe must be Hermitian in order to keep the eigenvalues real and to construct a self-consistent quantum theory. In addition to the open system approach by introducing environmental degrees of freedom to a small system, a global Hermitian Hamiltonian can also be generated through the dilation from a small Hilbert space. For example, a local non-Hermitian $\mathcal{P}T$-symmetric system can be simulated with a global Hermitian one by the Naimark dilation. Recently, by introducing local measurements and investigating the correlation functions of outcomes, the internal nonlocality in such dilated Hermitian systems has been revealed, but only for a special case with a twofold structure. In this paper, we extend such a discussion to the generalized case when the twofold structure breaks. The internal nonlocality is discussed with different correlation pictures and the corresponding correlation bounds. Our results provide a device-independent test of the reliability of the simulation in the global Hermiticity.

We present an analytical means of quantifying the fractional accumulation of the geometric phase for an optical vortex transiting a cylindrical lens. The standard fiber bundle of a sphere of modes is endowed with a supplementary product space at each point so that the beam waists and their positions can be explicitly tracked as functions of lens transit fraction. The method is applied to quantify the accumulation of the geometric phase across a single lens as a function of initial state and lens position within the beam. It can be readily applied to a series of lenses as well.

We examine the laser-assisted electron-positron pair-creation process from the quantum vacuum in the presence of a binding potential with one optically active bound electron. If this core electron is initially prepared in a coherent superposition state of two resonant bound states, the electronic phase properties between both state excitations can be transferred to the positron during the pair-creation process. For example, the periodic Rabi population exchange between both electronic states modulates the temporal growth of the pair-creation probability and also leads to an Autler-Townes split positron energy spectra. Even more astonishing, for the case of different phases, for which the internal electronic dynamics (in the absence of pair creation) is identical, the positron's creation probability is different, suggesting that the vacuum decay process can “sense” the phase and not just the occupation number of the core electron. The field theoretical model of the laser assisted pair-creation process with subsequent electron capture can be mapped exactly onto two mutually independent (single-electron) ionization-like processes. This mathematical equivalency permits us to derive analytical solutions for the time evolution of the vacuum decay process under the rotating-wave approximation.

We investigate theoretically the photoelectron momentum distribution (PMD) of ionized atoms irradiated by a linearly polarized intense laser, focusing on the holography interference patterns in PMD that carry important information of the initial wavefunction of a tunneled electron and its experienced atomic potential in rescattering. With the help of Dyson series and a semiclassical propagator, we calculate the scattering amplitudes in the cylindrical coordinate representation. In contrast to conventional recognitions that photoelectron holography is the interference of two branches of electron trajectories, however, we find strikingly that infinitely many semiclassical trajectories can be deflected by the combined Coulomb potential and laser field into the same final momentum. The initial momenta are found to be distributed on a ring-shaped curve in the transverse momentum plane and the initial positions of these trajectories are perpendicular to their initial momentum vectors. For the zero final transverse momentum, the above ring-source trajectories degenerate into the point-source axial caustic trajectories (or glory trajectories) and the quantum interference of these trajectories will dramatically alter the scattering amplitudes, which is termed the glory rescattering effect. By following Berry's spirit of uniform approximation for glory scattering in optics, we can finally derive a uniform formulation of the rescattering amplitude in the Bessel functions for the strong-field photoelectron holography patterns. Our results are in good agreement with solutions of the time-dependent Schrödinger equation and can account for recent photoelectron holography experiments. Important applications of our theory are also discussed.

In a binary quantum droplet, the interspecies attraction dominates over the intraspecies repulsions and the mean-field energy is unstable. The mechanical stability is restored by the repulsive Lee-Huang-Yang (LHY) energy [D. S. Petrov, Phys. Rev. Lett. 115, 155302 (2015)]. In the Bogoliubov theory of the binary quantum droplet, there are two branches of gapless excitations. The lower branch describes the phonon excitation and its energy is imaginary in the long-wavelength limit, implying dynamical instability. Recently, it was found that the phonon energy is renormalized by higher-order quantum fluctuations and the dynamical instability is removed [Q. Gu and L. Yin, Phys. Rev. B 102, 220503(R) (2020)]. In this paper, we study a binary quantum droplet in the path-integral formalism to construct an effective model with the correct phonon energy. By integrating out the upper excitation branch, we obtain an effective single-mode model describing density fluctuations, and derive the extended Gross-Pitaevskii equation (EGPE). In this approach, the LHY energy in the EGPE is purely positive without any assumption of neglecting the imaginary part. This effective single-mode model can be also used outside and close to the quantum droplet region such as in the LHY gas. Based on this effective model, we obtain the phase diagram of a uniform binary Bose system near the mean-field unstable point, which can be tested in experiments.

The present work is motivated by the recent experimental realization of the Townes soliton in an effective two-component Bose-Einstein condensate by B. Bakkali-Hassan et al. [Phys. Rev. Lett. 127, 023603 (2021)]. Here, we use a similar multicomponent platform to exemplify theoretically and numerically, within the mean-field Gross-Pitaevskii framework, the potential toward the experimental realization of a different fundamental wave structure, namely the Peregrine soliton. Leveraging the effective attractive interaction produced within the mixture's minority species in the immiscible regime, we illustrate how initialization of the condensate with a suitable power-law decaying spatial density pattern yields the robust emergence of the Peregrine wave in the absence and in the presence of a parabolic trap. We then showcase the spontaneous emergence of the Peregrine soliton via a suitably crafted wide Gaussian initialization, again both in the homogeneous case and in the trap scenario. It is also found that narrower wave packets may result in periodic revivals of the Peregrine soliton, while broader ones give rise to a cascade of Peregrine solitons arranged in a so-called Christmas-tree structure. Strikingly, the persistence of these rogue-wave structures is demonstrated in certain temperature regimes as well as in the presence of transversal excitations through three-dimensional computations in a quasi-one-dimensional regime. This proof-of-principle illustration is expected to represent a practically feasible way to generate and observe this rogue wave in realistic current ultracold atom experimental settings.