Stochastic differential equations (SDEs), which model uncertain phenomena as the time evolution of random variables, are exploited in various fields of natural and social sciences such as finance. Since SDEs rarely admit analytical solutions and must usually be solved numerically with huge classical-computational resources in practical applications, there is strong motivation to use quantum computation to accelerate the calculation. Here, we propose a quantum-classical hybrid algorithm that solves SDEs based on variational quantum simulation. We first approximate the target SDE by a trinomial tree structure with discretization and then formulate it as the time-evolution of a quantum state embedding the probability distributions of the SDE variables. We embed the probability distribution directly in the amplitudes of the quantum state whereas the previous studies took the square-root of the probability distribution in the amplitudes. Our embedding enables us to construct simple quantum circuits that simulate the time-evolution of the state for general SDEs. We also develop a scheme to compute the expectation values of the SDE variables and discuss whether our scheme can achieve quantum speedup for the expectation-value evaluations of the SDE variables. Finally, we numerically validate our algorithm by simulating several types of stochastic processes. Our proposal provides a new direction for simulating SDEs on quantum computers.

Photons are appealing as flying quantum bits due to their low-noise, long coherence times, light-speed transmission, and ease of manipulation at the single-qubit level using standard optical components such as beam splitters and waveguides. The challenge in optical quantum information processing has been the realization of two-qubit gates for photonic qubits due to the lack of highly efficient optical Kerr nonlinearities at the single-photon level. To date, only probabilistic two-qubit photonic controlled-phase gates based on linear optics and projective measurement using photon detectors have been demonstrated. Here we show that a high-fidelity frequency-encoded deterministic two-photon controlled-phase gate can be achieved by exploiting the strong photon-photon correlation enabled by photonic dimers, and the unique nonreciprocal photonic propagation in chiral quantum nanophotonic systems.

We address theoretically the problem of laser-induced dynamics of an electron, whose effective mass is position dependent (e.g., due to an effect of a semiconductor nanostructure environment). We derive the associated classical acceleration-gauge Hamiltonian $H_{\mathrm{AG}}\left(t\right)$ under the most general conditions, even without imposing the dipole approximation. It is shown that $H_{\mathrm{AG}}\left(t\right)$ possesses an intriguing structure arising due to the spatial dependence of the electronic mass. Subsequently, we restrict ourselves to a weak-field intensity regime, and derive the corresponding quantum mechanical acceleration-gauge Hamiltonian ${\widehat{H}}_{\mathrm{AG}}\left(t\right)$ which differs from its classical counterpart by an extra quantum term, $\widehat{\mathrm{QM}}$. Our theoretical findings are illustrated numerically by calculating the probability ${\left|T\left(E\right)\right|}^2$ of the resonance transmission of an electron through a model semiconductor nanostructure. It is demonstrated that the quantum mechanical $\widehat{\mathrm{QM}}$ term of ${\widehat{H}}_{\mathrm{AG}}\left(t\right)$ does often affect crucially the profile of ${\left|T\left(E\right)\right|}^2$.

We report the realization of Bose-Einstein condensation (BEC) of metastable helium atoms using an in-vacuum coil magnetic trap and a crossed-beam optical dipole trap. A quadrupole-Ioffe configuration magnetic trap made from in-vacuum hollow copper tubes provides fast switching times while generating traps with a 10-G bias, without compromising optical access. The bias enables in-trap one-dimensional Doppler cooling to be used, which is the only cooling stage between the magneto-optic trap and the optical dipole trap. This allows direct transfer to the dipole trap without the need for any additional evaporative cooling in the magnetic trap. The entire experimental sequence takes 3.3 s, with essentially pure BECs observed with $\sim {10}^6$ atoms after evaporative cooling in the dipole trap.

The superradiant phase transition represents an important quantum phenomenon that shows collective excitations based on the coupling between atoms and cavity modes. Spin-orbit coupling is another quantum effect which is induced by the interaction of the atomic internal degrees of freedom and center-of-mass momentum. In this work we consider the cavity-assisted dynamical spin-orbit coupling which comes from the combination of these two effects. It can generate a series of interesting quantum phenomena such as the flat spectrum and the discontinuity of the excitation energy spectrum around the critical point of the quantum phase transition. We further discuss the influence of atom decay and nonlinear coupling on the phase diagram. The atom decay suppresses the discontinuity of the phase diagram and the nonlinear coupling can break the symmetric properties of the phase transition. Our work provides a theoretical method to research the rich quantum phenomena in this dynamic many-body system.

This work completes the program started by I. Bialynicki-Birula and Z. Bialynicka-Birula [Uncertainty relation for photons, Phys. Rev. Lett. 108, 140401 (2012); Heisenberg uncertainty relation for photons, Phys. Rev. A 86, 022118 (2012); Heisenberg uncertainty relation for relativistic electrons, New J. Phys. 21, 073036 (2019)] to derive the Heisenberg uncertainty relation for relativistic particles. Sharp uncertainty relations for massive relativistic particles with spin 0 and spin 1 are derived. The main conclusion is that the uncertainty relations for relativistic bosons are markedly different from those for relativistic fermions. The uncertainty relations for bosons are based on the energy density. It is shown that the uncertainty relations based on the time component of the four-current, as we have done previously for electrons, are untenable because they lead to contradictions.

Quantum backaction from weak measurement affects the behavior of quantum systems. We consider a nonlinear driven Duffing oscillator system implementation in a nonlinear optical cavity, and we show that the choice of phase setting $\varphi$ for a laser used in measurement can change the dissipation for the spread variables of the quantum state. This can considerably increase the energy absorbed via the energy channel of the spread variables and enhance quantum effects. This suggests novel applications to quantum control, as we demonstrate, including an example in which the energy in the spread variables allows for a dynamical tunneling between energetically separated dynamical stead-states.

Entanglement concurrence has been widely used for featuring entanglement in quantum experiments. As an entanglement monotone it is related to specific quantum Tsallis entropy. Our goal in this paper is to propose a parametrized bipartite entanglement monotone which is named as $q$-concurrence inspired by general Tsallis entropy. We derive an analytical lower bound for the $q$-concurrence of any bipartite quantum entanglement state by employing positive partial transposition criterion and realignment criterion, which shows an interesting relationship to the strong separability criteria. The parametrized entanglement monotone is used to characterize bipartite isotropic states. Finally, we provide a computational method to estimate the $q$-concurrence for any entanglement by superposing two bipartite pure states. It shows that the superposition operations can at most increase one ebit for the $q$-concurrence in the case that the two states being superposed are biorthogonal or one-sided orthogonal. These results reveal a series of phenomena about the entanglement, which may be interesting in quantum communication and quantum information processing.

We discuss a general bipartitelike representation and Schmidt decomposition of an arbitrary pure state of $N$ indistinguishable fermions, based on states of $M<N$ and $(N-M)$ fermions. It is directly connected with the reduced $M$- and $(N-M)$-body density matrices (DMs), which have the same spectrum in such states. The concept of $M$-body entanglement emerges naturally in this scenario, generalizing that of one-body entanglement. Rigorous majorization relations satisfied by the normalized $M$-body DM are then derived, which imply that the associated entropy will not increase, on average, under a class of operations which have these DMs as postmeasurement states. Moreover, such entropy is an upper bound to the bipartite entanglement entropy generated by a class of operations which map the original state to a bipartite state of $M$ and $N-M$ effectively distinguishable fermions. Analytic evaluation of the spectrum of $M$-body DMs in some strongly correlated fermionic states is also provided.

We study the process of laser-assisted dissociative recombination of an electron with a molecular cation using a semiclassical approach. In the region outside a reaction sphere the electron motion in the combined laser and Coulomb fields is treated classically. Within the sphere the laser-field effects are neglected, and the recombination probability is obtained from quantum-mechanical cross sections calculated for the laser-free process. Specific calculations are performed for dissociative recombination of ${\mathrm{H}}_2^{+}$ in the field of the intensity 2.09 GW/${\mathrm{cm}}^2$ and the wavelength $22.8\mu \mathrm{m}$. In the energy region above 1 meV the cross section is significantly enhanced compared with the field-free case due to the Coulomb focusing effect. The influence of the indirect process due to electron capture into Rydberg states is also investigated. Although the Rydberg resonances are washed out due to the field effects, they influence significantly the magnitude of the dissociative recombination cross section.

We theoretically investigate the elliptical high-order harmonic generation from the H${}_2^{+}$ molecule driven by the orthogonally polarized two-color laser field by numerically solving the two-dimensional time-dependent $\mathrm{Schr}\ddot{\text{o}}\mathrm{dinger}$ equation. The results show that the odd-order harmonics in the $x$ component and the even-order harmonics in the $y$ component can be generated with the specific alignment angle $\theta =0^{\circ }$ for the different intensity ratios of the laser fields. The harmonic intensity distribution and ellipticity distribution at the different intensity ratios of the laser fields and the alignment angles differ significantly from each other. The result also shows that the ellipticity-tunable high-order harmonics can be generated through adjusting the intensity ratio of the laser fields and the alignment angles. Further analyses show that the amplitude ratio and the phase difference of the $x$ and $y$ components of the harmonics are the origin of the ellipticity of the harmonics in general. The two-center interference effect can also affect the ellipticity of the harmonics. The results show that the ellipticity of the harmonics can be used as a potential tool to probe the position of the minimum. The results we obtained can be useful for the optimization of elliptically polarized XUV radiation generation.

We start from the Maxwell-Bloch equations that govern the dynamics of Fabry-Perot lasers and, considering a doubled cavity, generalize our traveling wave formalism to the case in which the two-level medium does not fill the cavity but occupies only a portion of it. We linearize these equations and focus on the adiabatic elimination of both atomic fluctuations. Next, we restrict our attention to free running lasers under resonant conditions and analyze amplitude and phase instabilities. The examination of the unstable domain leads to the conclusion that the multimode Fabry-Perot instability arises near threshold only when the ratio of the longitudinal to the transverse atomic relaxation rate is substantially smaller than unity. This result agrees with our previous study in the limit of adiabatic elimination of the atomic polarization fluctuations only. We describe the self-pulsing behavior that arises from the multimode instability, and exhibits hysteretic behavior when the pump parameter is swept forward and backward. Finally, we investigate the single-mode instability and show that in the Fabry-Perot case there is no longer the correspondence between single-mode and multimode instabilities that is well known in the case of ring lasers. We confirm that in the case of resonant Fabry-Perot lasers the single-mode amplitude instability arises very far from threshold.

The question of whether an electron radiating its energy away during the interaction with a laser can reach the region of highest intensity with energy high enough to make a number of different phenomena observable is one of the most studied and most important in strong field quantum electrodynamics. Here a simple analytical estimate for an average electron energy evolution is proposed and benchmarked against particle-in-cell simulations. Furthermore, these results are used to estimate the electron and laser pulse properties required to make vacuum Cherenkov emission observable.

Three-dimensional mapping of microscopic surface structures is important in many applications of technology and research, including areas as diverse as microfluidics, MEMS, and geoscience. However, on the nanoscale, using established techniques for such imaging can be extremely challenging. Scanning helium microscopy is a technique that uses neutral helium atoms as a probe, enabling completely nondestructive imaging. The technique is broadly applicable and ideal for many otherwise difficult-to-image materials, such as insulators, ultrathin nanocoatings, and biological samples. Here we present a method for implementation and operation of a stereo helium microscope, by applying the photometric stereo method of surface reconstruction to helium microscopy. Four detectors around the sample are typically required, but we show how sample rotation can be used to perform stereo reconstruction with a single-detector instrument, or to improve the quality of the reconstructed surface by increasing the number of independent measurements. We examine the quality of the reconstructed surface and show that for low aspect ratio good absolute height is recovered. For features with height/width $\sim 1$ the shape of the surface is still recovered well (8% error) despite multiple scattering and masking of the helium beam by surface topography. Therefore, it is possible to perform accurate reconstruction of the shape of nanoscale structures with a height to width ratio of at least unity.

Long-lived storage of arbitrary transverse multimodes is important for establishing a high-channel-capacity quantum network. Most of the pioneering works focused on atomic diffusion as the dominant impact on the retrieved pattern in an atom-based memory. In this work, we demonstrate that the unsynchronized Larmor precession of atoms in the inhomogeneous magnetic field dominates the distortion of the pattern stored in a cold-atom-based memory. We find that this distortion effect can be eliminated by applying a strong uniform polarization magnetic field. By mapping signal light into a spin wave between a pair of clock states, the destructive interference between different spin-wave components is diminished, and the stored localized patterns are synchronized further in a single spin-wave component; then, an obvious enhancement in preserving patterns for a long time is obtained. The reported results are promising for studying transverse multimode decoherence in optical storage and may find potential applications in the field of high-dimensional quantum networks in the future.

Using the profound interferometric philosophy of weak-value amplification, we propose a simple, general, and robust polarization method for the amplification and quantification of small magnitudes of all possible polarization anisotropy effects in a single experimental embodiment. The approach is experimentally realized by introducing a weak coupling between the polarization degree of freedom of light and the path degree of freedom in a Mach-Zehnder interferometer in the presence of a weak anisotropy effect. Real and imaginary weak-value amplifications of different polarization anisotropy effects are manifested as characteristic changes in the relevant Stokes vector elements at the exit port of the interferometer, which follow orthogonal trajectories in the Poincaré sphere. The proof-of-concept experiment demonstrates that by using this scheme, one can faithfully extract and quantify an anisotropy parameter that is smaller than the typical sensitivity of measurement of a given Stokes parameter of a traditional polarimeter by a large weak-value amplification factor. This opens up the possibility of a sample measuring weak-value polarimeter for studying the rich variety of fundamental optical effects and for materials characterization and precision metrology.

Non-Hermitian topological systems are the newest additions to the growing field of topological matter. In this work, we report the light-driven exceptional physics in a multi-Weyl semimetal. The driving is not only a key ingredient to control the position of the exceptional contours (ECs); light also has the ability to generate new ECs. Interestingly, we also demonstrate topological charge distribution and Lifshitz transition, which are controllable by the driving field in such generated ECs. Our findings present a promising platform for the manipulation and control over exceptional physics in non-Hermitian topological matter.

Reconnecting vortices in a superfluid allows for the energy transfer between different length scales and its subsequent dissipation. The present picture assumes that the dynamics of a reconnection is driven mostly by the phase of the order parameter, and this statement can be justified in the case of Bose-Einstein Condensates (BECs), where vortices have a simple internal structure. Therefore, it is natural to postulate that the reconnection dynamics in the vicinity of the reconnection moment is universal. This expectation has been confirmed in numerical simulations for BECs and experimentally for the superfluid ${}^4\mathrm{He}$. Not much has been said about this relation in the context of Fermi superfluids. In this Letter, we aim to bridge this gap, and we report our findings, which reveal that the reconnection dynamics conforms with the predicted universal behavior across the entire BCS-BEC crossover. The universal scaling also survives for spin-imbalanced systems, where unpaired fermions induce a complex structure of the colliding vortices.

As a universal theory of physics, quantum mechanics must assign states to every level of description of a system—from a full microscopic description all the way up to an effective macroscopic characterization—and also to describe the interconnections among them. Assuming that we only have a coarse-grained access to a physical system, here we show how to assign to it a microscopic description that abides by all macroscopic constraints. In order to do that, we employ general coarse-graining maps, allowing our approach to be used even when the split between system and environment is not obvious. As a by-product, we show how effective nonlinear dynamics can emerge from the linear quantum evolution, and we readily apply it to a state discrimination task.