Orbital angular momentum (OAM) of photons has applications both in classical and quantum information due to its features of optical vortex and infinite dimensions. This paper studies the interference effects of optical vortex beams carrying mixed, conjugate, and single-mode OAM states based on the Sagnac interferometer with light sources of a laser and single photon. We compare our results with numerical simulations and show that the light intensity distribution and phase characteristics can directly characterize the absolute value of the topological charge (TC) carried by vortex beams. Furthermore, our scheme can also classify the photon with positive and negative signs of TC in the mixed mode OAM state by changing the relative phase. The results not only extend the manipulation methods for high-dimensional quantum states, but also lay a solid foundation for the application of vortex beams in a single-photon field.

Bosonic quantum codes redundantly encode quantum information in the states of a quantum harmonic oscillator, making it possible to detect and correct errors. Schrödinger cat codes—based on the superposition of two coherent states with opposite displacements—can correct phase-flip errors induced by dephasing, but they are vulnerable to bit-flip errors induced by particle loss. Here, we develop a bosonic quantum code relying on squeezed cat states, i.e., cat states made of a linear superposition of displaced-squeezed states. Squeezed cat states allow to partially correct errors caused by particle loss, while at the same time improving the protection against dephasing. We present a comprehensive analysis of the squeezed cat code, including protocols for code generation and elementary quantum gates. We characterize the effect of both particle loss and dephasing and develop an optimal recovery protocol that is suitable to be implemented on currently available quantum hardware. We show that with moderate squeezing, and using typical parameters of state-of-the-art quantum hardware platforms, the squeezed cat code has a resilience to particle loss errors that significantly outperforms that of the conventional cat code.

We apply a Gaussian state formalism to track fluctuating perturbations that act on the position and momentum quadrature variables of a harmonic oscillator. Following a seminal proposal by Tsang and Caves [Phys. Rev. Lett. 105, 123601 (2010)], Einstein-Podolsky-Rosen correlations with the quadrature variables of an ancillary harmonic oscillator are leveraged to significantly improve the estimates as relevant sensor variables can be arbitrarily squeezed while evading adverse effects from the conjugate, antisqueezed variables. Our real-time analysis of the continuous monitoring of the system employs a hybrid quantum-classical description of the quantum probe and the unknown classical perturbations, and it provides a general formalism to establish the achievements of the sensing scheme and how they depend on different parameters.

We study multiple ionization in proton collisions with water, methane, and ammonia molecules using an independent-atom model. Previous work on total (net) capture and ionization cross sections is extended to treat the multiple-ionization channels explicitly. We present the theoretical framework to treat charge-state correlated processes within the independent-atom-model approach, which uses the geometric screening introduced for different molecular geometries and orientations. A comparison of results is made for the target molecules ${\text{H}}_2\text{O}, {\text{CH}}_4$, and ${\text{NH}}_3$ with an emphasis on $q$-fold electron removal. Coincident measurements of produced molecular fragments can be used to estimate this quantity. We find very good agreement for the model calculations for the water molecule, where data exist for $q=1–4$. For methane we observe reasonable agreement for $q=1,2$ and for ammonia only for $q=1$, i.e., the experimental data show little support for a direct multiple-ionization channel in the latter case.

We present a study of interspecies Feshbach resonances in ultracold ${}^7\mathrm{Li}{\text{−}}^{133}\mathrm{Cs}$ Bose-Bose mixtures. We locate ten interspecies resonances in three different spin-state combinations. By comparing to coupled-channel calculations, we assign six of the resonances to $s$-wave channels and the rest to $p$-wave channels. We use the $s$-wave resonances to refine the ground-state potentials of LiCs in the coupled-channel calculations and then obtain an accurate characterization of the scattering and bound-state properties of the mixtures. Our results will be useful for future experiments with ultracold ${}^7\mathrm{Li}{\text{−}}^{133}\mathrm{Cs}$ mixtures.

The recent experimental realization of optical tweezer arrays of ultracold molecules provides a versatile platform for exploring molecular phases of matter. Here we show that by programming tweezers, the dipolar interactions in an optical tweezer ladder could be tailored to implement a generalized Su-Schrieffer-Heeger model. Through calculating topological invariants, nonlocal string-order parameters, many-particle ground-state degeneracy, and entanglement spectrum, we demonstrate that this ladder at the single-particle level supports two different chiral topological phases and at the many-particle level features two different interacting topological phases and, respectively, possesses much richer topological edge states. We also discuss the detection of these topological phases and their robustness to systematic imperfections. Further generalization to a high dimension could offer opportunities for preparing diverse ultracold molecular topological phases.

We analytically derive the transport tensor of thermal conductivity in an ultracold, but not yet quantum degenerate, gas of Bosonic lanthanide atoms using the Chapman-Enskog procedure. The tensor coefficients inherit an anisotropy from the anisotropic collision cross section for these dipolar species, manifest in their dependence on the dipole moment, dipole orientation, and $s$-wave scattering length. These functional dependences open up a pathway for control of macroscopic gas phenomena via tuning of the microscopic atomic interactions. As an illustrative example, we analyze the time evolution of a temperature hot spot which shows preferential heat diffusion orthogonal to the dipole orientation, a direct consequence of anisotropic thermal conduction.

In polymer science, cross-linking of polymer chains yields a substantially modified system compared with the one-dimensional (1D) constituent chains, due to the increase of dimensionality and effective seeding by defects (cross-linking sites). Inspired by this concept, we analyze topological features of a unit cell of a generalized topological mesh comprised of several 1D Su-Schrieffer-Heeger (SSH) lattices cross-linked via a single site. The coupling site functions as a defect with protected states in the trivial regime and induces edges inside the bulk with protected localized states centered around it in the topological regime. When more than two lattices are coupled by the defect, namely, a graph dimensionality larger than one, the crossed chains support two types of localized eigenstates around the defect. One type is highly controllable by modifying the cross-linking strength, enabling broad tuning of eigenenergies from being submerged in the bulk band to becoming highly isolated and protected. We show that these unique features can be explained by an equivalence of the system to an SSH chain coupled nonreciprocally to an external reservoir, yielding a unique pseudospectrum for both the bulk and localized states, with spatially symmetric eigenstates. Applying non-Hermiticity by adding gain and loss to alternating sites, relevant, for example, to a possible realization of topological coupled-laser fabric, we observe an abrupt transition of the topologically protected midgap state from antilocalized to localized near the defect. By changing the gain-loss parameters, we observe a cascaded spatial symmetry breaking of the supported states at exceptional points where parity-time symmetry is broken, for both the localized and the bulk states, exhibiting various phases.

For two orthonormal bases of a $d$-dimensional complex Hilbert space, the notion of complete incompatibility was introduced recently by De Bièvre, [Phys. Rev. Lett. 127, 190404 (2021)]. In this paper, we introduce the notion of $s$-order incompatibility with positive integer $s$ satisfying $2\le s\le d+1.$ In particular, $(d+1)$-order incompatibility just coincides with the complete incompatibility. We establish some relations between $s$-order incompatibility, minimal support uncertainty, and rank deficiency of the transition matrix. As an example, we determine the incompatibility order of the discrete Fourier transform with any finite dimension.

We study spin-nematic squeezing in a spinor Bose-Einstein condensate and use it to probe dynamical quantum phase transitions. We show that the quench dynamics of the spin-nematic squeezing exhibits a nonanalytical change with respect to a final quadratic Zeeman energy, and demonstrate that the squeezing detects not only the ground state phase diagram, but also the excited state quantum phase transition. We further analyze the dynamic stabilization of the system and present its relation to the dynamical quantum phase transitions. Our results are applicable to the spinor condensates with both of the sodium and rubidium atoms.

The orbital degree of freedom plays an important role in understanding exotic phenomena of strongly correlated materials. In this work, we study strongly correlated ultracold bosonic gases coupled to a high-finesse cavity, pumped by a blue-detuned laser in the transverse direction. By controlling the reflection of the pump laser, we find that atoms can be selectively transferred to the odd-parity $p$-orbital band or to the even-parity $d$-orbital band of a two-dimensional square lattice, accompanied by pronounced cavity-photon excitations. By interacting with the cavity field, atoms self-organize to form stable higher-orbital superfluid and Mott-insulating phases with orbital-density waves, as a result of cavity-induced orbital-flip hoppings. Our study opens a route to manipulate orbital degrees of freedom in strongly correlated quantum gases via coupling to optical cavities.

We present a detailed study about ion-atom-atom three-body recombination in hydrogen and deuterium plasmas based on classical trajectory calculations in hyperspherical coordinates. Our results, due to the predominant role of the long-range charged-induced dipole interaction, indicate that ${\mathrm{H}}_2{}^{+}$ and ${\mathrm{D}}_2{}^{+}$ are the main reaction products in the case of hydrogen and deuterium plasmas, respectively. In addition, we find a more steep energy-dependent reaction rate when the collision energy surpasses the dissociation energy of the molecular ion, thus entering a new dynamical regime dominated by short-range interactions.

Cat states, which were initially proposed to manifest macroscopic superpositions, play an outstanding role in fundamental aspects of quantum dynamics. In addition, they have potential applications in quantum computation and quantum sensing. However, cat states are vulnerable to dissipation, which puts the focus of cat-state generation on higher speed and increased robustness. Dissipative cat-state generation is a common approach based on the nonlinear coupling between a lossy pump field and a half-frequency signal field. In such an approach, the pump field is usually kept in equilibrium, which limits the cat-state generation. We show that the equilibrium requirement can be removed by leveraging a synchronous pump method. In this nonequilibrium regime, the speed of the cat-state generation can be increased by one order of magnitude, and the robustness to single-photon loss can be enhanced. The realization of synchronous pumps is discussed for both time-multiplexed systems and standing modes.

The quantum regression theorem is one of the central results in open quantum systems and is extensively used for computing multi-point correlation functions. Traditionally it is derived for two-time correlators in the Markovian limit employing the Schrödinger picture. In this paper we make use of the Heisenberg picture to derive the quantum regression theorems for multi-time correlation functions, which in the special limit reduce to the well-known two-time regression theorem. For the multi-time correlation function we find that the regression theorem takes the same form as it takes for the two-time correlation function with a mild restriction that one of the times should be greater than all other time variables. Interestingly, the Heisenberg picture also allows us to derive an analog of regression theorem for out-of-time-ordered correlators. We further extend our study for the case of non-Markovian dynamics and report the modifications to the standard quantum regression theorem. We illustrate all of the above results using the paradigmatic dissipative spin-boson model.

Universality of motion under gravity, the equivalence principle, is violated for quantum particles. Here, we study the time it takes for a quantum particle to scatter from the gravitational potential and show that the scattering time, formulated here using the opportune Bohmian formulation, acts as an indicator of the equivalence principle violation. The scattering times of wave packets are distinctive enough to distinguish between the Bohmian and Copenhagen interpretations. The scattering time of monoenergetic stationary states, formulated here as a modification of the Bohmian time by probability undercurrents, turns out to be a sensitive probe of the equivalence principle violation. We derive the quantum scattering times and analyze equivalence principle violating terms systematically. We discuss the experimental setup needed for measuring the violation, and describe implications of a possible measurement for time in quantum theory, including the tunneling time.

We extend quantum noise spectroscopy (QNS) of amplitude control noise to settings where dephasing noise or detuning errors make significant contributions to qubit dynamics. Previous approaches to characterize amplitude noise are limited by their vulnerability to low-frequency dephasing noise and static detuning errors, which can overwhelm the target control noise signal and introduce bias into estimates of the amplitude noise spectrum. To overcome this problem, we leverage optimal control to identify a family of amplitude control waveforms that optimally suppress low-frequency dephasing noise and detuning errors, while maintaining the spectral concentration in the amplitude filter essential for spectral estimation. The waveforms found via numerical optimization have surprisingly simple analytic forms, consisting of oscillating sine waves obeying particular amplitude and frequency constraints. In numerically simulated QNS experiments, these waveforms demonstrate superior robustness, enabling accurate estimation of the amplitude noise spectrum in regimes where existing approaches are biased by low-frequency dephasing noise and detuning errors.

We perform optimal-control-theory calculations to determine the minimum number of two-qubit controlled-not (cnot) gates needed to perform quantum state preparation and unitary operator synthesis for few-qubit systems. By considering all possible gate configurations, we determine the maximum achievable fidelity as a function of quantum circuit size. This information allows us to identify the minimum circuit size needed for a specific target operation and enumerate the different gate configurations that allow a perfect implementation of the operation. We find that there are a large number of configurations that all produce the desired result, even at the minimum number of gates. We also show that the number of entangling gates can be reduced if we use multiqubit entangling gates instead of two-qubit cnot gates, as one might expect based on parameter counting calculations. In addition to treating the general case of arbitrary target states or unitary operators, we apply the numerical approach to the special case of synthesizing the multiqubit Toffoli gate. This approach can be used to investigate any other specific few-qubit task and provides insight into the tightness of different bounds in the literature.

Continuous clocks, i.e., clocks that measure time in a continuous manner, are regarded as an essential component of sensing technology. Precision and recurrence time are two basic features of continuous clocks. In this paper, in the framework of quantum estimation theory various models for continuous quantum clocks are proposed, and all tools of quantum estimation theory are employed to seek the characteristics of clocks with high precision and long recurrence time. Then, in a resource-based approach, the performances of the proposed models are compared. It is shown that quantum clocks based on an $n$ two-qubit system not only can have better precision than quantum clocks based on a $2n$ one-qubit system but also support long recurrence time. Finally, it is shown that while employing $n$ entangled qubits improves the precision of clocks by a factor of $1/\sqrt{n}$, it inevitably worsens the recurrence time of the clock.

We study how different types of quantum correlations can be established as the consequence of a generalized entanglement swapping protocol where, starting from two Bell pairs (1,2) and (3,4), a general quantum measurement [denoted by a positive operator-valued measure (POVM)] is performed on the pair (2,3), which results in creating quantum correlation in (1,4) shared between two spatially separated observers. Contingent upon using different kinds of POVMs, we show generation or destruction of different quantum correlations in the pairs (1,4), (1,2), and (3,4). This thus reflects nontrivial transfer of quantum correlations from the pairs (1,2) and (3,4) to the pair (1,4). As an offshoot, this paper provides an operational tool to generate different types of single parameter families of quantum correlated states [for example, entangled but not Einstein-Podolsky-Rosen (EPR) steerable, or EPR steerable but not Bell nonlocal, or Bell nonlocal] by choosing different quantum measurements in the basic entanglement swapping setup. We further extend our paper by taking mixed initial states shared by the pairs (1,2) and (3,4). Finally, we study network nonlocality in our scenario. Here, we find the appropriate POVM measurement for which the generated correlation demonstrates or does not demonstrate network nonlocality for the whole range of the measurement parameter.

Recently a widely used computation expression for quantum Fisher information was shown to be discontinuous at the parameter points where the rank of the parametric density operator changes. The quantum Cramér-Rao bound can be violated on such singular parameter points if one uses this computation expression for quantum Fisher information. We point out that the discontinuity of the computation expression of quantum Fisher information is accompanied with the unboundedness of the symmetric logarithmic derivation operators, based on which the quantum Fisher information is formally defined and the quantum Cramér-Rao bound is originally proved. We argue that the limiting version of the quantum Cramér-Rao bound still holds when the parametric density operator changes its rank by closing the potential loophole of involving an unbounded SLD operator in the proof of the bound. Moreover, we analyze a typical example of the quantum statistical models with parameter-dependent rank.