Squeezed-state interferometry plays an important role in quantum-enhanced optical phase estimation, as it allows the estimation precision to be improved up to the Heisenberg limit by using ideal photon-number-resolving detectors at the output ports. Here we show that for each individual $N$-photon component of the phase-matched coherent $\otimes$ squeezed vacuum input state, the classical Fisher information always saturates the quantum Fisher information. Moreover, the total Fisher information is the sum of the contributions from each individual $N$-photon component, where the largest $N$ is limited by the finite number resolution of available photon counters. Based on this observation, we provide an approximate analytical formula that quantifies the amount of lost information due to the finite photon number resolution; e.g., given the mean photon number $\overline{n}$ in the input state, over 96% of the Heisenberg limit can be achieved with the number resolution larger than $5\overline{n}$.

Due to the dominant electron capture by positrons from the molecular shell and the spatial dephasing across the shell width, a powerful diffraction effect universally underlies the positronium (Ps) formation from fullerenes. This results in trains of resonances in the Ps formation cross section as a function of the positron beam energy, producing structures in recoil momenta in analogy with classical single-slit diffraction fringes in the configuration space. This work opens a hitherto unknown avenue of Ps spectroscopy with nanomaterials and motivates level-differential measurements.

We demonstrate Rabi oscillations in nonlinear ionization of argon by an intense femtosecond extreme ultraviolet (XUV) laser field produced by high-harmonic generation. We monitor the formation of $\mathrm{A}{\mathrm{r}}^{2+}$ as a function of the time delay between the XUV pulse and an additional near-infrared (NIR) femtosecond laser pulse, and show that the population of an $\mathrm{A}{\mathrm{r}}^{+*}$ intermediate resonance exhibits strong modulations both due to an NIR laser-induced Stark shift and XUV-induced Rabi cycling between the ground state of $\mathrm{A}{\mathrm{r}}^{+}$ and the $\mathrm{A}{\mathrm{r}}^{+*}$ excited state. Our experiment represents a direct experimental observation of a Rabi-cycling process in the XUV regime.

We study the set of almost-quantum correlations and their refinements in the simplest tripartite Bell scenario where each party is allowed to perform two dichotomic measurements. In contrast to its bipartite counterpart, we find that there already exist facet Bell inequalities that witness almost-quantum correlations beyond quantum theory in this simplest tripartite Bell scenario. Furthermore, we study the relation between the almost-quantum set and the hierarchy of supersets to the quantum set due to Navascués-Pironio-Acín (NPA) [Phys. Rev. Lett. 98, 010401 (2007)]. While the former lies between the first and the third level of the NPA hierarchy, we find that its second level does not contain and is not contained within the almost-quantum set. Finally, we investigate the hierarchy of refinements to the almost-quantum set due to Moroder et al. [Phys. Rev. Lett. 111, 030501 (2013)], which converges to the set of quantum correlations producible by quantum states having positive partial transposition. This allows us to consider (approximations of) the “biseparable” subsets of the almost-quantum set as well as of the quantum set of correlations, and thereby gain further insights into the subtle similarities and differences between the two sets. In addition, they allow us to identify candidate Bell-like inequalities that can serve as device-independent witnesses for genuine tripartite entanglement.

Heisenberg's uncertainty relation has been extensively studied in spirit of its well-known original form, in which the inaccuracy measures used exhibit some controversial properties and don't conform with quantum metrology, where the measurement precision is well defined in terms of estimation theory. In this paper, we treat the joint measurement of incompatible observables as a parameter estimation problem, i.e., estimating the parameters characterizing the statistics of the incompatible observables. Our crucial observation is that, in a sequential measurement scenario, the bias induced by the first unbiased measurement in the subsequent measurement can be eradicated by the information acquired, allowing one to extract unbiased information of the second measurement of an incompatible observable. In terms of Fisher information we propose a kind of information comparison measure and explore various types of trade-offs between the information gains and measurement precisions, which interpret the uncertainty relation as surplus variance trade-off over individual perfect measurements instead of a constraint on extracting complete information of incompatible observables.

We consider a quantum system dynamics caused by successive selective and nonselective measurements of the probe coupled to the system. For the finite measurement rate ${\tau }^{-1}$ and the system-probe interaction strength $\gamma$ we derive analytical evolution equations in the stroboscopic limit $\tau \to 0$ and ${\gamma }^2\tau =\mathrm{const}$, which can be considered as a deviation from the Zeno subspace dynamics on a longer time scale $T\sim {\left({\gamma }^2\tau \right)}^{-1}\gg {\gamma }^{-1}$. Nonlinear quantum dynamics is analyzed for selective stroboscopic projective measurements of an arbitrary rank. Nonselective measurements are shown to induce the semigroup dynamics of the system-probe aggregate. Both nonlinear and decoherent effects become significant at the time scale $T\sim {\left({\gamma }^2\tau \right)}^{-1}$, which is illustrated by a number of examples.

A quantum-feedback-based scheme is proposed for generating multipartite entanglements of Rydberg atoms in a dissipative optical cavity. The Rydberg blockade mechanism efficiently prevents double excitations of the system, which is further exploited to speed up the stabilization of an entangled state with a single Rydberg state excitation. The corresponding feedback operations are greatly simplified, since only one regular atom needs to be controlled during the whole process, irrespective of the number of particles. The form of the entangled state is also adjustable via regulating the Rabi frequencies of driving fields. Moreover, a relatively long lifetime of the high-lying Rydberg level guarantees a high fidelity in a realistic situation.

We study ${}^{87}\mathrm{Rb}$ cold collisions in a static magnetic field and a single-color radio-frequency (RF) field by employing the multichannel quantum defect theory in combination with the Floquet method to solve the two-body time-dependent Schrödinger equation. Our results show that RF fields can modify the two-body scattering length by a large scale through Feshbach resonances in both low- and high-static magnetic-field regimes. Such RF-induced Feshbach resonances can be applied to quenching experiments or control of interactions in spinor condensates. Here, we also show that, analogously to photoassociation, RF fields can also associate cold atoms into molecules at a useful rate.

We present a detailed theoretical investigation on strong-field ionization of polar (CO and NO) as well as nonpolar molecules (${\mathrm{N}}_2, {\mathrm{O}}_2$, and ${\mathrm{CO}}_2$). Our results indicate that accounting for the Stark correction in the molecular tunneling ionization theory leads to overall fairly good agreements with numerical solutions of the time-dependent Schrödinger equation. Furthermore, we show that the effect of dynamic core-electron polarization, in general, has a weak influence on the angle-dependent ionization probability. However, in the case of CO we confirm the recent finding by B. Zhang, J. Yuan, and Z. Zhao [Phys. Rev. Lett. 111, 163001 (2013)] that accounting for dynamic core-polarization is crucial to achieving an overall good agreement with experiments.

The Sagnac interferometry has widely been used to measure rotation frequency. Beyond the conventional single-particle scheme, we propose a multiparticle scheme via Bose condensed atoms. In our scheme, an ensemble of entangled two-state Bose atoms are moved in a ring via a state-dependent rotating potential, and then the atoms are recombined for interference via Ramsey pulses. The phase accumulation time is determined by the state-dependent rotating potential. The ultimate rotation sensitivity can be improved to the Heisenberg limit if the initial internal degrees of freedom are entangled. By implementing parity measurement, the ultimate measurement precision can be saturated, and the achieved measurement precisions approach the Heisenberg limit. Our results provide a promising way to exploit many-body quantum entanglement in precision rotation sensing.

Temperature fluctuations of an optical resonator underlie a fundamental limit of its cavity stability. Here we show that the fundamental temperature fluctuations of a high-$Q$ microresonator can be suppressed remarkably by pure optical means without cooling the device temperature. An optical wave launched into the cavity is able to produce strong photothermal backaction which dramatically suppresses the spectral intensity of temperature fluctuations and squeezes its overall level by orders of magnitude. The proposed photothermal temperature squeezing is expected to significantly improve the stability of optical resonances, with potentially profound impact on broad applications of high-$Q$ cavities in sensing, metrology, and nonlinear and quantum optics.

The possibility of observing many-body localization of ultracold atoms in a one-dimensional optical lattice is discussed for random interactions. In the noninteracting limit, such a system reduces to single-particle physics in the absence of disorder, i.e., to extended states. In effect, the observed localization is inherently due to interactions and is thus a genuine many-body effect. In the system studied, many-body localization manifests itself in a lack of thermalization visible in temporal propagation of a specially prepared initial state, in transport properties, in the logarithmic growth of entanglement entropy, and in statistical properties of energy levels.

Consider local dephasing processes of a qubit that interacts with a structured reservoir of frequency modes or a thermal bath, with Ohmic-like spectral density (SD). It is known that non-Markovian evolution appears uniquely above a temperature-dependent critical value of the Ohmicity parameter and non-Markovianity can be induced by properly engineering the external environment. In the same scenario, we find regular patterns in the flow of quantum information: Alternate directions appear in correspondence with periodic intervals of the Ohmicity parameter ${\alpha }_0$. The information flows back into the system over long times at zero temperature for $2+4n<{\alpha }_0<4+4n$, where $n=0,1,2,...,$ and at nonvanishing temperatures for $3+4n<{\alpha }_0<5+4n$. Under special conditions, backflow of information appears also for nonvanishing, even natural values of the Ohmicity parameter, at zero temperature, and for odd natural values at nonvanishing temperatures. Otherwise, the long-time information flows into the environment. In the transition from vanishing to arbitrary nonvanishing temperature, the long-time backflow of information is stable for $3+4n<{\alpha }_0<4+4n$, while it is reversed for $2+4n<{\alpha }_0<3+4n$ and $4+4n<{\alpha }_0<5+4n$. The patterns in the information flow are not altered if the low-frequency Ohmic-like profiles of the SDs are perturbed with additional factors that consist in arbitrary powers of logarithmic forms. Consequently, the flow of information can be controlled, directed, and reversed over long times by engineering a wide variety of reservoirs that includes and continuously departs from the Ohmic-like structure at low frequencies. Non-Markovianity and recoherence appear according to the same rules along with the backflow of information.

We review a time-dependent version of the Schrieffer-Wolff transformation that accounts for real-time control of system parameters, soon to be rendered possible on a broad basis due to technical progress. The dispersive regime of $N$ multilevel systems coupled to a cavity via a Jaynes-Cummings interaction is extended to the most general case. As a concrete example we rigorously apply the technique to dispersive two-qubit gates in a superconducting architecture, showing that fidelities based on previous models are off by up to ${10}^{-2}$, which is certainly relevant for high-fidelity gates compatible with fault-tolerant quantum information devices. A closed analytic form for the error depending on the target evolution closes our work.

In continuous-variables quantum key distribution with coherent states, the advantage of performing the detection by using standard telecoms components is counterbalanced by the lack of a stable phase reference in homodyne detection due to the complexity of optical phase-locking circuits and to the unavoidable phase noise of lasers, which introduces a degradation on the achievable secure key rate. Pilot-assisted phase-noise estimation and postdetection compensation techniques are used to implement a protocol with coherent states where a local laser is employed and it is not locked to the received signal, but a postdetection phase correction is applied. Here the reduction of the secure key rate determined by the laser phase noise, for both individual and collective attacks, is analytically evaluated and a scheme of pilot-assisted phase estimation proposed, outlining the tradeoff in the system design between phase noise and spectral efficiency. The optimal modulation variance as a function of the phase-noise amount is derived.

The standard approach to fault-tolerant quantum computation is to store information in a quantum error correction code, such as the surface code, and process information using a strategy that can be summarized as distill then synthesize. In the distill step, one performs several rounds of distillation to create high-fidelity logical qubits in a magic state. Each such magic state provides one good $T$ gate. In the synthesize step, one seeks the optimal decomposition of an algorithm into a sequence of many $T$ gates interleaved with Clifford gates. This gate-synthesis problem is well understood for multiqubit gates that do not use any Hadamards. We present an in-depth analysis of a unified framework that realizes one round of distillation and multiqubit gate synthesis in a single step. We call these synthillation protocols, and show they lead to a large reduction in resource overheads. This is because synthillation can implement a general class of circuits using the same number of $T$ states as gate synthesis, yet with the benefit of quadratic error suppression. This general class includes all circuits primarily dominated by control-control-$Z$ gates, such as adders and modular exponentiation routines used in Shor's algorithm. Therefore, synthillation removes the need for a costly round of magic state distillation. We also present several additional results on the multiqubit gate-synthesis problem. We provide an efficient algorithm for synthesizing unitaries with the same worst-case resource scaling as optimal solutions. For the special case of synthesizing controlled unitaries, our techniques are not just efficient but exactly optimal. We observe that the gate-synthesis cost, measured by $T$ count, is often strictly subadditive. Numerous explicit applications of our techniques are also presented.

The ${\mathrm{TaO}}^{+}$ molecular ion is proposed as a candidate system for detecting signatures of charge-parity-violating physics beyond the standard model of elementary particles. The electron electric dipole moment (EDM) effective electric field $E_{\text{eff}}=20.2$ GV/cm, the nucleon-electron scalar-pseudoscalar (SPS) interaction constant $W_S=17.7$ kHz, and the nuclear magnetic quadrupole interaction constant $W_M=0.45\times {10}^{33}$ Hz/($e$ ${\mathrm{cm}}^2$) are found to be sizable $\mathcal{P},\mathcal{T}$-odd enhancements. The ratio of the leptonic and semileptonic enhancements differs strongly from the one for the ThO system which may provide improved limits on the electron EDM, $d_e$, and the SPS coupling constant, $C_S$. ${\mathrm{TaO}}^{+}$ is found to have a ${}^3{\mathrm{\Delta }}_1$ electronic ground state like the previously proposed ${\mathrm{ThF}}^{+}$ molecular ion, but an order of magnitude smaller parallel $G$-tensor component which makes it less vulnerable to systematic errors in experiment.

We study the statics and dynamics of a stable, mobile, three-dimensional matter-wave spherical quantum ball created in the presence of an attractive two-body and a very small repulsive three-body interaction. The quantum ball can propagate with a constant velocity in any direction in free space and its stability under a small perturbation is established numerically and variationally. In frontal head-on and angular collisions at large velocities two quantum balls behave like quantum solitons. Such collision is found to be quasielastic and the quantum balls emerge after collision without any change of direction of motion and velocity and with practically no deformation in shape. When reflected by a hard impenetrable plane, the quantum ball bounces off like a wave obeying the law of reflection without any change of shape or speed. However, in a collision at small velocities two quantum balls coalesce to form a larger ball which we call a quantum-ball breather. We point out the similarity and difference between the collision of two quantum and classical balls. The present study is based on an analytic variational approximation and a full numerical solution of the mean-field Gross-Pitaevskii equation using the parameters of ${}^7\mathrm{Li}$ atoms.