Textbook quantum mechanics treats time as a classical parameter and not as a quantum observable with an associated Hermitian operator. For this reason, to make sense of usual time-energy uncertainty relations such as $\mathrm{\Delta }t\mathrm{\Delta }E\gtrsim \hslash$, the term $\mathrm{\Delta }t$ must be interpreted as a time interval and not as a time measurement uncertainty due to quantum noise. However, quantum clocks allow for a measurement of the “time at which an event happens” by conditioning the system's evolution on an additional quantum degree of freedom. Within this framework we derive here two uncertainty relations that relate the uncertainty in the quantum measurement of the time at which a quantum event happens on a system to its energy uncertainty.

We report orthopositronium $\left(o\text{−}\mathrm{Ps}\right)$ thermalization observed in cryogenic silica aerogel cooled from room temperature to 25 K. It was observed that the $o\text{−}\mathrm{Ps}$ thermalization rate gets slower as $o\text{−}\mathrm{Ps}$ itself is colder than room temperature. This energy dependence can be explained based on a model where the efficiency of kinetic energy exchange between $o\text{−}\mathrm{Ps}$ and silica is determined by the de Broglie wavelength of $o\text{−}\mathrm{Ps}$. The present measurement confirmed that a cooling method which utilizes the thermalization process at cryogenic temperatures followed by laser cooling is applicable for the efficient production of an $o\text{−}\mathrm{Ps}$ Bose-Einstein condensate.

Quantum nonlocality is a prominent discrepancy when we compare quantum physics with classical physics, and it manifests in different forms, one of which is quantum steering. Quantum steering refers to a correlation produced from a bipartite entangled state between the local measurement outcomes of one party and the postmeasurement states of the other. Combining with uncertainty relation, local measurements can be used to distinguish whether a quantum state is steerable. Thus, this method can be treated as an effective steering criterion. In this work, we certify this steering criterion based on the local uncertainty relation by an all-optical setup with a mixed state which consists of two Bell-like states. Furthermore, we also testify that the quantum steering criterion based on the local uncertainty relation is not only superior to the linear steering criterion but also superior to the steering criterion based on the entropic uncertainty relation in our scenario. Our efforts may promote the use of this criterion in quantum information processing tasks.

The reaction coordinate (RC) technique is emerging as a significant tool in the study of quantum dissipative dynamics and quantum thermodynamics. With the objective to further establish this tool, here we explore to what extent the method can capture non-Markovian dynamics of open quantum systems. As a case study, we focus on the pure decoherence model of a spin coupled to a harmonic reservoir. We compare the spin dynamics and measures for non-Markovianity from the exact analytical solution to simulations based on the RC method at the level of a second-order quantum master equation. We find that the RC method can quantitatively capture non-Markovian effects at strong system-bath coupling and for structured baths. This is rationalized by the fact that the collective RC bath mode, which is made part of the system, maintains system-bath correlations. Lastly, we apply our RC method and study the spin-boson model in the non-Markovian regime.

A quantum internet, i.e., a global interconnection of quantum devices, is the long-term goal of quantum communications and has so far been based on two-dimensional systems (qubits). Recent years have seen a significant development of high-dimensional quantum systems (qudits). While qudits present higher photon information efficiency and robustness to noise, their use in quantum networks presents experimental challenges due to the impractical resources required in high-dimensional quantum repeaters. Here, we show that such challenges can be met via the use of standard quantum optical resources, such as weak coherent states or weak squeezed states, and linear optics. We report a concrete design and simulations of an entanglement swapping scheme for three- and four-dimensional systems, showing how the network parameters can be tuned to optimize secret key rates and analyzing the enhanced noise robustness at different dimensions. Our work significantly simplifies the implementation of high-dimensional quantum networks, fostering their development with current technology.

We investigate the properties of a spin-imbalanced and rotating unitary Fermi gas. Using a density functional theory, we provide insight into states that emerge from a competition between Abrikosov lattice formation, spatial phase separation, and the emergence of the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state. A confrontation of the experimental data [M. Zwierlein et al., Science 311, 492 (2006)] with theoretical predictions provides a remarkable qualitative agreement. In the case of gas confined in a harmonic trap, the phase separation into a superfluid core populated by the Abrikosov lattice and a spin-polarized corona is the dominant process. Changing confinement to a boxlike trap reverts the spatial location of the component: gas being in the normal state is surrounded by superfluid threaded by quantum vortices. The vortex lattice no longer exhibits the triangular symmetry, and the emergence of exotic geometries may be an indirect signature of the FFLO-like state formation in the system.

The realization and detection of various phase transitions in interacting two-leg bosonic flux ladders are at the frontier of the present theoretical and experimental research in condensed-matter physics. We develop a biased two-leg Bose-Hubbard flux ladder model and first achieve the ground states and phase transition conditions of this system by the mean-field approach and variational analysis. Rich phases are revealed, including two different kinds of plane-wave phase, i.e., plane wave I (characterized with one single energy minimum of the energy band) and plane wave II (characterized with two nondegenerate local energy minima of the energy band), and interestingly the asymmetry vortex phase with the breaking of both $Z_2$ reflection symmetry and translational symmetry of space, which is characterized by the vortex with imbalanced density distributions on two legs. Moreover, the corresponding quantum phases can also be distinguished by the order parameters and the excitation spectra of the plane-wave phase intuitively. Furthermore, we demonstrate that this biased ladder system also makes it possible to realize a different dynamical asymmetric vortex state, which shows a dynamical supersolidlike property.

Development of attosecond laser technology allows us to measure electron dynamics such as photoionization delays between different species or electronic states. In general, the measured photoionization phase is a mixture of the spectral phase of the extreme ultraviolet (XUV) pulse and the atomic phases inherent to the optical transitions. Hence, it is difficult to disentangle these phases independently. Here we separate these phases by using an XUV attosecond pulse train containing both even and odd harmonic orders, generated by an 800- and 400 nm laser pulse, in the presence of the infrared 800-nm pulse. We measure the photoelectron angular distributions as a function of two independently controlled delays, the XUV-IR and the 800–400 nm delays, with attosecond time resolution. We analyze the photoelectron angular distributions to determine the relative amplitudes and phases of each angular momentum component. Using an in situ technique, we determine the phases of the harmonic orders and thereby completely determine the atomic phases. Using the obtained atomic phases and amplitudes, we reconstruct the real and imaginary parts of the continuum wave functions associated with three individual photoionization pathways.

Recently, it was demonstrated that the concept of a spectral singularity (SS) can be generalized to waves propagating in nonlinear media, like matter waves or electromagnetic waves in Kerr media. The corresponding solutions represent nonlinear currents sustained by a localized linear complex potential in a nonlinear Schrödinger equation. A key feature allowing for the nonlinear generalization of a SS is the possibility to reduce a nonlinear current to the linear limit, where a SS has the unambiguous definition. In the meantime, known examples of nonlinear modes bifurcating from linear spectral singularities are few and belong to the specific class of constant-amplitude waves. Here we propose to extend the class of nonlinear SSs by incorporating solutions whose amplitudes are inhomogeneous. We show that the continuation from the linear limit requires a deformation of the complex potential, and this deformation is not unique. Examples include the deformation preserving the gain-and-loss distribution and the deformation preserving the geometry of the potential. For the case example of a rectangular potential, we demonstrate that the nonlinear currents can be divided into two types: solutions of the first type bifurcate from the linear spectral singularities, and solutions of the second type cannot be reduced to the linear limit.

In the general theory of quantum measurement, one associates a positive-semidefinite operator on a $d$-dimensional Hilbert space to each of the $n$ possible outcomes of an arbitrary measurement. In the special case of a projective measurement, these operators are pairwise Hilbert-Schmidt orthogonal, but when $n>d$, orthogonality is restricted by positivity. This restriction allows us to more precisely state the quantum adage: information gain of a system is always accompanied by unavoidable disturbance. Specifically, we investigate three properties of a measurement with Lüders rule updating: its disturbance, a measure of how the expected postmeasurement state deviates from the input; its measurement strength, a measure of the intrinsic information producing capacity of the measurement; and its orthogonality, a measure of the degree to which the measurement operators differ from an orthonormal set. These quantities satisfy an information-disturbance tradeoff relation that highlights the additional role played by orthogonality. Finally, we assess several classes of measurements on these grounds and identify symmetric informationally complete quantum measurements as the unique quantum analogs of a perfectly informative and nondisturbing classical ideal measurement.

We present an exactly solvable model for synthetic anyons carrying non-Abelian flux. The model corresponds to a two-dimensional electron gas in a magnetic field with a specific spin interaction term, which allows only fully aligned spin states in the ground state; the ground state subspace is thus twofold degenerate. This system is perturbed with identical solenoids carrying a non-Abelian gauge potential. We explore dynamics of the ground state as these solenoids are adiabatically braided and show they behave as anyons with a non-Abelian flux. Such a system represents a middle ground between the ordinary Abelian anyons and the fully non-Abelian anyons.

We study the polaron quasiparticle in a one-dimensional Bose gas. In the integrable case described by the Yang-Gaudin model, we derive an exact result for the polaron mass in the thermodynamic limit. It is expressed in terms of the derivative with respect to the density of the ground-state energy per particle of the Bose gas without the polaron. This enables us to find high-order power series for the polaron mass in the regimes of weak and strong interaction.

We analyze multipartite correlations in a generalized Dicke model involving two optical modes interacting with an ensemble of two-level atoms. In particular, we examine correlations beyond the standard bipartite entanglement and derive exact results in the thermodynamic limit. The model presents two superradiant phases involving the spontaneous breaking of either a ${\mathbb{Z}}_2$ or a U(1) symmetry. The latter is characterized by the emergence of a Goldstone excitation, found to significantly affect the correlation profiles. Focusing on the correlations between macroscopic subsystems, we analyze both the mutual information and the entanglement of formation for all possible bipartitions among the optical and matter degrees of freedom. It is found that while each mode entangles with the atoms, the bipartite entanglement between the modes is zero, and they share only classical correlations and quantum discord. We also study the monogamy of multipartite entanglement and show that there exists genuine tripartite entanglement, i.e., quantum correlations that the atoms share with the two modes but that are not shared with them individually, only in the vicinity of the critical lines. Our results elucidate the intricate correlation structures underlying superradiant phase transitions in multimode systems.

We investigate the influence of environment noise on the control cost and the quantum speed limit time (QSLT) in the process of almost-exact state transmission (AEST) through a spin chain under pulse control. The chain is immersed in its surrounding non-Markovian, finite-temperature heat baths. We find that AEST can be realized in weak system-bath coupling, low temperature, and strong non-Markovian baths under effective external control. Correspondingly, the control cost and QSLT increase with increasing bath temperature and coupling strength. It is noticeable that non-Markovianity from the baths can be helpful to reduce the control cost and shorten the QSLT. Furthermore, we find that there exists a trade-off between the control cost and transmission fidelity and that higher fidelity requires higher cost. In addition, the minimum control cost has been found to obtain certain transmission fidelity.

The channel fading induced in the ocean quantum links is a major obstacle restricting the performance of ocean quantum key distribution. To determine the ultimate limits at which secret bits (and entanglement) can be distributed via a seawater medium, we propose an analytical model for ocean quantum links to derive the probability distribution of the transmittance, which characterizes the evolution of the quantum state over the fading channel. The proposed model includes the effects of absorption, scattering, turbulence, and ocean thermal noise due to background light. Our comprehensive numerical analysis of several practical scenarios encompasses both pure-loss bounds and thermal-loss bounds, with a submarine at various depths and in various oceans on earth. Besides identifying ultimate limits, we present a security analysis of coherent-state and squeezed-state protocols, showing the secret key rate of both the asymptotic case and finite-size regimes.

Quantum systems can be controlled by other quantum systems in a reversible way, without any information leaking to the outside of the system-controller compound. Such coherent quantum control is deterministic, is less noisy than measurement-based feedback control, and has potential applications in a variety of quantum technologies, including quantum computation, quantum communication, and quantum metrology. Here we introduce a coherent feedback protocol, consisting of a sequence of identical interactions with controlling quantum systems, that steers a quantum system from an arbitrary initial state towards a target state. We determine the broad class of such coherent feedback channels that achieve convergence to the target state, and then stabilize as well as protect it against noise. Our results imply that also weak system-controller interactions can counter noise if they occur with suitably high frequency. We present an example of a control scheme that does not require knowledge of the target state encoded in the controllers, which could be the result of a quantum computation. It thus provides a mechanism for autonomous, purely quantum closed-loop control.

The measurement of circular dichroism (CD) has widely been exploited to distinguish the different enantiomers of chiral structures. It has been applied to natural materials (e.g., molecules) as well as to artificial materials (e.g., nanophotonic structures). However, especially for chiral molecules the signal level is very low and increasing the signal-to-noise ratio is of paramount importance to either shorten the necessary measurement time or to lower the minimum detectable molecule concentration. As one solution to this problem, we propose here to use quantum states of light in CD sensing to reduce the noise below the shot noise level encountered when using coherent states of light. Through a multiparameter estimation approach, we identify the ultimate quantum limit of the precision in CD sensing, allowing for general schemes including additional ancillary modes. We show that the ultimate quantum limit can be achieved by various optimal schemes. These include using a pair of Fock-state probes in a direct sensing configuration and pairs of twin beams in an ancilla-assisted sensing configuration, for both of which photon number-resolved detection is shown to be the optimal measurement. These optimal schemes offer a significant quantum enhancement even in the presence of some additional system loss. The near optimality of a scheme using a single twin beam in a direct sensing configuration is also shown for cases where the actual CD signal is very small. Alternative optimal schemes involving single-photon sources and detectors are also proposed. This work paves the way for further investigations of quantum metrological techniques in chirality sensing.

Diabatic quantum annealing (DQA) is an alternative algorithm to adiabatic quantum annealing that can be used to circumvent the exponential slowdown caused by small minima in the annealing energy spectrum. We present the locally suppressed transverse-field (LSTF) protocol, a heuristic method for making stoquastic optimization problems compatible with DQA. We show that, provided an optimization problem intrinsically has magnetic frustration due to inhomogeneous local fields, a target qubit in the problem can always be manipulated to create a double minimum in the energy gap between the ground and first excited states during the evolution of the algorithm. Such a double energy minimum can be exploited to induce diabatic transitions to the first excited state and back to the ground state. In addition to its relevance to classical and quantum algorithmic speedups, the LSTF protocol enables DQA proof-of-principle and physics experiments to be performed on existing hardware, provided independent controls exist for the transverse qubit magnetization fields. We discuss the implications on the coherence requirements of the quantum annealing hardware when using the LSTF protocol, considering specifically the cases of relaxation and dephasing. We show that the relaxation rate of a large system can be made to depend only on the target qubit, presenting opportunities for the characterization of the decohering environment in a quantum annealing processor.

We perform a measurement of the tune-out wavelength, ${\lambda }_0$, between the $D_1$, $6^2{S}_{1/2}\to 6^2{P}_{1/2}$, and $D_2$, $6^2{S}_{1/2}\to 6^2{P}_{3/2}$, transitions for ${}^{133}\mathrm{Cs}$ in the ground hyperfine state $(F=3,m_F=+3)$. At ${\lambda }_0$, the frequency-dependent scalar polarizability is zero leading to a zero scalar ac Stark shift. We measure the polarizability as a function of wavelength using Kapitza-Dirac scattering of a ${}^{133}\mathrm{Cs}$ Bose-Einstein condensate in a one-dimensional optical lattice, and determine the tune-out wavelength to be ${\lambda }_0=880.21790{\left(40\right)}_{\text{stat}}{\left(8\right)}_{\text{sys}}$ nm. From this measurement we determine the ratio of reduced matrix elements to be ${\left|\langle 6P_{3/2}\parallel d\parallel 6S_{1/2}\rangle \right|}^2/{\left|\langle 6P_{1/2}\parallel d\parallel 6S_{1/2}\rangle \right|}^2=1.9808\left(2\right)$. This represents an improvement of a factor of 10 over previous results derived from excited-state lifetime measurements. We use the present measurement as a benchmark test of high-precision theory.

Four-dimensional imaging of charge migration is crucial to the understanding of several ubiquitous processes in nature. The present work focuses on imaging of charge migration in an oriented epoxypropane: a chiral molecule. A linearly polarized pulse is used to induce the charge migration, which is imaged by time-resolved x-ray diffraction. It is found that the total time-resolved diffraction signals are significantly different for both enantiomers. Furthermore, a connection between time-resolved x-ray diffraction and the electronic continuity equation is discussed by analyzing the time-dependent diffraction signal and the time derivative of the total electron density in the momentum space.