A single photon has many physical degrees of freedom (DOF) that can carry the state of a high-dimensional quantum system. Nevertheless, only a single DOF is usually used in any specific demonstration. Furthermore, when more DOF are being used, they are analyzed and measured one at a time. We introduce a two-qubit information system, realized by two degrees of freedom of a single photon: polarization and time. The photon arrival time is divided into two time bins representing a qubit, while its polarization state represents a second qubit. The time difference between the two time bins is created without an interferometer at the picosecond scale, which is much smaller than the detector's response time. The two physically different DOF are analyzed simultaneously by photon bunching between the analyzed photon and an ancilla photon. Full two-qubit states encoded in single photons were reconstructed using quantum state tomography, both when the two DOF were entangled and when they were not, with fidelities higher than 96%.

Containing the capacity to record both amplitude and phase information of the light field, holography is of great importance in science and technology. Here, we present robust holography via second-order interference, considering both single-photon states and coherent states. Temporal amplitude and phase distribution carried by a weak coherent state are reconstructed experimentally. By comparison between holography using first-order interference and second-order interference, the robustness against phase noise of our method is verified. Besides, information about the state can be directly retrieved, with no complex algorithm required.

We perform high-precision calculations of the hyperfine structure for $n{S}_{1/2}$ and $n{P}_{1/2}$ states of the alkali-metal atoms Rb, Cs, and Fr across the principal quantum number $n$ and study the trend in the size of the correlations. Our calculations are performed in the all-orders correlation potential method. We demonstrate that the relative correlation corrections fall off quickly with $n$ and tend towards constant and nonzero values for highly excited states. This trend is supported by experiments, and we utilize the smooth dependence on $n$ to make high-accuracy predictions of the hyperfine constants, with uncertainties to within 0.1% for most considered $S_{1/2}$ states of Rb and Cs.

The 4503 rovibronic term values belonging to the mutually perturbed $A{}^1{\mathrm{\Sigma }}_u^{+}$ and $b{}^3{\mathrm{\Pi }}_u$ states of ${\mathrm{Cs}}_2$ were extracted from laser-induced fluorescence (LIF) $A\sim b\to X{}^1{\mathrm{\Sigma }}_g^{+}$ Fourier-transform spectra with the 0.01-${\mathrm{cm}}^{-1}$ uncertainty. The experimental term values of the $A{}^1{\mathrm{\Sigma }}_u^{+}\sim b{}^3{\mathrm{\Pi }}_u$ complex covering the rotational levels $J\in [4,395]$ in the excitation energy range $[9655,13630]{\mathrm{cm}}^{-1}$ were involved into coupled-channel (CC) deperturbation analysis. The deperturbation model takes explicitly into account spin-orbit coupling of the $A{}^1{\mathrm{\Sigma }}_u^{+}\left(A{0}_u^{+}\right)$ and $b{}^3{\mathrm{\Pi }}_{0_u}^{+}\left(b{0}_u^{+}\right)$ states as well as spin-rotational interaction between the $\mathrm{\Omega }=0$, 1, and 2 components of the $b{}^3{\mathrm{\Pi }}_{{\mathrm{\Omega }}_u}^{+}$ state. The ab initio relativistic calculations on the low-lying electronic states of ${\mathrm{Cs}}_2$ were accomplished in the framework of Fock-space relativistic coupled cluster (FSRCC) approach to provide the interatomic potentials of the interacting $A{0}_u^{+}$ and $b{0}_u^{+}$ states as well as the relevant $A\sim b$ spin-orbit coupling function. To validate the present CC deperturbation analysis solely obtained by energy-based data, the $A\sim b\to X\left(v_X^{\prime \prime }\right)$ LIF intensity distributions were measured and compared with their theoretical counterparts obtained by means of the nonadiabatic vibrational wave functions of the $A\sim b$ complex and the FSRCC $A\sim b\to X$ transition dipole moments calculated by the finite-field method.

The spectrum of a cw field the phase of which experiences a periodic sawtooth modulation is analyzed. Two types of the sawtooth phase modulation are considered. One is created by combining many harmonics of the fundamental frequency. The second is produced by an electro-optic modulator fed by the relaxation oscillator, which generates a voltage slowly rising during charging of the energy storage device and dropping fast due to discharge by a short circuit. It is proposed to filter out the main spectral component of the sawtooth phase-modulated field. This filtering produces short pulses from the phase-modulated cw field. The duty cycle of this train is equal to the modulation period, while duration of the pulses depends on the rate of the phase drop. In the case of harmonics, this duration is $4N+2$ shorter than the period of the fundamental frequency, where $N$ is the number of the harmonics. In the case of the charge and discharge, duration of the pulses is close to $T_D/2$, where $T_D$ is a drop time of the phase in the discharge period. Depending on the modulation frequency, the proposed method is capable to produce pulses with duration ranging from nanoseconds to a fraction of a picosecond.

In driven-dissipative systems, the presence of a strong symmetry guarantees the existence of several steady states belonging to different symmetry sectors. Here we show that when a system with a strong symmetry is initialized in a quantum superposition involving several of these sectors, each individual stochastic trajectory will randomly select a single one of them and remain there for the rest of the evolution. Since a strong symmetry implies a conservation law for the corresponding symmetry operator on the ensemble level, this selection of a single sector from an initial superposition entails a breakdown of this conservation law at the level of individual realizations. Given that such a superposition is impossible in a classical stochastic trajectory, this is a a purely quantum effect with no classical analog. Our results show that a system with a closed Liouvillian gap may exhibit, when monitored over a single run of an experiment, a behavior completely opposite to the usual notion of dynamical phase coexistence and intermittency, which are typically considered hallmarks of a dissipative phase transition. We discuss our results on a coherently driven spin ensemble with a squeezed superradiant decay, a simple model that presents a wealth of nonergodic dynamics.

Machine learning techniques based on artificial neural networks have been successfully applied to solve many problems in science. One of the most interesting domains of machine learning, reinforcement learning, has a natural applicability for optimization problems in physics. In this paper, we use deep reinforcement learning and chopped random basis optimization to solve an optimization problem based on the insertion of an off-center barrier in a quantum Szilard engine. We show that by using designed protocols for the time dependence of the barrier strength, we can achieve an equal splitting of the wave function (1/2 probability to find the particle on either side of the barrier) even for an asymmetric Szilard engine in such a way that no information is lost when measuring which side the particle is found. This implies that the asymmetric nonadiabatic Szilard engine can operate with the same efficiency as the traditional Szilard engine with adiabatic insertion of a central barrier. We compare the two optimization methods and demonstrate the advantage of reinforcement learning when it comes to constructing robust and noise-resistant protocols.

We study the role that the global phase plays in quantum operations. Previous theoretical works suggested that the optimal (minimum) times to realize $\mathrm{SU}\left(n\right)$ quantum operations with different global phases are generally different. Here, we experimentally constructed two SU(2) operations with different global phases, i.e., $U$ and $-U$, in optimal times. Then, utilizing nuclear magnetic resonance interferometry, we measured these phases and observed the global phase's effect on the optimal times of these two operations. Our result further clarifies that the effect that the global phase has on unitary operations is not only mathematical, but also physical. In addition, this work has potential applications in many areas, such as designing time-optimal controls in quantum systems.

The time-dependent pseudo-Hermitian formulation of quantum mechanics allows one to study open system dynamics in analogy to Hermitian quantum systems. In this setting, we show that the notion of holonomic quantum computation can equally be formulated for pseudo-Hermitian systems. Starting from a degenerate pseudo-Hermitian Hamiltonian we show that, in the adiabatic limit, a non-Abelian geometric phase emerges which realizes a pseudounitary quantum gate. We illustrate our findings by studying a pseudo-Hermitian gain-loss system which can be written in the form of a tripod Hamiltonian by using the biorthogonal representation. It is shown that this system allows for arbitrary pseudo-$U\left(2\right)$ transformations acting on the dark subspace of the system.

Photoionization microscopy (PM) is an electron imaging method designed for the measurement of the outgoing flux of slow electrons produced by photoionization of atoms in the presence of an external uniform static electric field. The high resolution of PM allows the observation of spatial quantum interference structures which are directly related to the squared modulus of the excited electron's wave function. The PM's range of interest lies above the saddle-point energy, where continuum Stark states are degenerate with quasibound ones (resonances). A principal aim of PM is to provide access to the wave functions of the latter, which in hydrogen atoms ionize exclusively via tunneling (in contrast to the continuum states where the electron escapes freely above the potential barrier). In nonhydrogenic atoms, however, quasibound states are coupled with the continuum ones. Among other consequences, this leads to comparable resonant and continuum excitation strengths and the weakening or disappearance of the resonant manifestations from the recorded PM images. Here we examine theoretically the possibility of bypassing these difficulties by applying two-excitation-pathway interference techniques. For this first case-study we employ the hydrogen atom but we, nevertheless, simulate a nonhydrogenic situation by selecting hydrogenic Stark resonances whose excitation strengths are comparable to or even smaller than the continuum ones. Specifically, we consider the interaction of ground-state atoms with an ω/2ω bichromatic laser field inducing one- and two-photon transitions to the final Stark states. It is shown that, under certain conditions and by appropriately adjusting the intensities of the two laser fields and their relative phase, the uncovering of resonant manifestations from PM images may indeed be achieved. Further work concerning theoretical extensions to complex atoms and possible experimental realizations are also discussed.

Spin squeezing (SS) is a recognized resource for realizing measurement precision beyond the standard quantum limit $\propto 1/\sqrt{N}$. The rudimentary one-axis twisting (OAT) interaction can facilitate SS and has been realized in diverse experiments, but it cannot achieve extreme SS for precision at the Heisenberg limit $\propto 1/N$. Aided by deep reinforcement learning (DRL), we discover size-independent universal rules for realizing nearly extreme SS with a OAT interaction using merely a handful of rotation pulses. More specifically, only six pairs of pulses are required for up to ${10}^4$ particles, while the time taken to reach extreme SS remains on the same order of the optimal OAT squeezing time, which makes our scheme viable for experiments that reported OAT squeezing. This Rapid Communication highlights the potential of DRL for controlled quantum dynamics.

We present analytically and numerically the spectrum of high harmonic emission generated by twisted electrons in the presence of linearly polarized light. Ensuing transitions from electronic continuum states with orbital angular momentum to bound states give rise to circularly polarized attosecond pulses. For central collisions with twisted wave packets, continuum-bound transitions are subject to dipole selection rules. For noncentral collisions, a crossover from circularly to linearly polarized emission occurs for increasing impact parameter due to the transverse topology of twisted wave packets.

That quantum correlations can be generated over time between the spin and the position of a quantum walker is indisputable. The creation of bipartite entanglement has also been reported for two-walker systems. In this scenario, however, since the global state lies in a fourpartite Hilbert space, the question arises as to whether genuine multipartite entanglement may develop in time. Also, since the spatial degrees of freedom can be viewed as a noisy channel for the two-spin part, one may wonder how other nonclassical aspects, such as Bell nonlocality, Einstein-Podolsky-Rosen steering, quantum discord, and symmetrical quantum discord, evolve in time during the walk. The lack of analytical and numerical evidences which would allow one to address these questions is possibly due to the usual computational difficulties associated with the recursive nature of quantum walks. Here, we work around this issue by introducing a simplified Gaussian model which proves to be very accurate within a given domain and powerful for analytical studies. Then, for an instance involving two noninteracting quantum walkers, whose spins start in the singlet state, we quantify the aforementioned nonclassical features as a function of time, and evaluate violations of both realism and related aspects of locality. In addition, we analyze situations in which the initial two-spin state is affected by white noise. The typical scenario found is such that while genuine fourpartite entanglement increases over time, all the investigated nonclassical features vanish (suddenly or asymptotically) except realism-based nonlocality. Moreover, realism is prevented for all finite times. Our findings open perspectives for the understanding of the dynamics of quantum resources in quantum walks.

The quantization of plasmons has been analyzed mostly under the assumption of an infinite-size bulk medium interacting with the electromagnetic field. We reformulate it for finite-size media, such as metallic or dielectric nanostructures, highlighting sharp differences. By diagonalizing the Hamiltonian by means of a Lippmann-Schwinger equation, we show the contribution of two sets of bosonic operators, one stemming from medium fluctuations and one from the electromagnetic field. The results apply to general models including dissipative and dispersive responses.

In traditional open quantum systems, the baths are usually traced out so that only the system information is left in the equations of motion. However, recent studies reveal that using only the system degrees of freedom can be insufficient. In this work, we develop a stochastic $c$-number Langevin equation method which can conveniently access the bath information. In our approach, the studied quantities are the expectation values of operators which can contain both system operators and bath operators. The dynamics of the operators of interest is formally divided into separate system and bath parts, with auxiliary stochastic fields. After solving the independent stochastic dynamics of the system part and the bath part, we can recombine them by taking the average over these stochastic fields to obtain the desired quantities. Several applications of the theory are highlighted, including the pure dephasing model, the spin-boson model, and an optically excited quantum dot coupled to a bath of phonons.

We study prepare-and-measure experiments where the sender (Alice) receives trusted quantum inputs but has an untrusted state-preparation device and the receiver (Bob) has a fully untrusted measurement device. A distributed-sampling task naturally arises in this scenario, where the goal is for Alice and Bob to reproduce the statistics of his measurements on her quantum inputs using a fixed communication channel. Their performance of this task can certify quantum communication (QC), and this is formalized by measurement-device-independent QC witnesses. Furthermore, we prove that QC can provide an advantage (over classical communication) for distributed sampling if and only if Bob's measurements are incompatible. This gives an operational interpretation to measurement incompatibility and motivates a generalized notion of it related to a subset of quantum states. Our findings have both fundamental and applied implications.

In this work, we show how electron-vibrational mode coupling can be used to drive maximally entangled states. The physical system consists of two pairs of quantum dots, each pair with a single electron able to tunnel between the dots, thus encoding a qubit. The electron-vibrational mode coupling, described by the strength parameter $g$, yields to an effective electron-electron interaction, responsible for the formation of a maximally entangled quantum state. Both the formation time and the relative phase of the aforementioned state are strongly dependent on $g$. The quantum dynamics exhibits a nonmonotonic behavior as $g$ increases, an effect explained through an effective Hamiltonian that takes into account high-order transition processes.

Quantum networking based on optical Gaussian states, although promising in terms of scalability, is hindered by the fact that their entanglement cannot be distilled via Gaussian operations. We show that optomechanics, and particularly the possibility to measure the mechanical degree of freedom in an integrable system, can address this problem. Here, one of the optical modes of a two-mode squeezed vacuum is injected into a single-sided Fabry-Pérot cavity and nonlinearly coupled to a mechanical oscillator. Afterwards, the position of the oscillator is measured using pulsed optomechanics and homodyne detection. We show that this measurement can supply non-Gaussian entangled states frequently enough to enable scalable entanglement distillation. Moreover, it can conditionally increase the initial entanglement under an optimal radiation-pressure interaction strength, which corresponds to an effective unsharp measurement of the photon number inside the cavity. We show how the resulting entanglement enhancement can be verified by using a standard teleportation procedure.

Different nonlocal quantum correlations of entanglement, steering and Bell nonlocality are defined with the help of local hidden state and local hidden variable models. Considering their unique roles in quantum information processing, it is of importance to understand the individual nonlocal quantum correlation as well as their relationship. Here, we investigate the effects of amplitude damping decoherence on different nonlocal quantum correlations. In particular, we have theoretically and experimentally shown that the entanglement sudden death phenomenon is distinct from those of steering and Bell nonlocality. In our scenario, we found that all the initial states present sudden death of steering and Bell nonlocality, while only some of the states show entanglement sudden death. These results suggest that the environmental effect can be different for different nonlocal quantum correlations and, thus, it provides distinct operational interpretations of different quantum correlations.

The quantum erasure channel models phenomena such as loss or leakage of qubits. Using quantum codes, we can recover from such errors. In this paper, we are interested in studying the performance of two-dimensional color codes over the quantum erasure channel. Our approach makes use of the local equivalence between color codes and surface codes. We propose a variety of decoding algorithms for color codes over the erasure channel. First, we propose algorithms that decode by projecting the erasures on the color to surface codes. Then, instead of directly decoding on the color code or on the equivalent copies of surface codes, we decode jointly on the color code and the equivalent surface codes. We observe a threshold of 44.3% for the color code on the square octagonal lattice.