We consider a qubit governed by a sequence of weak measurements, with the measurement strength modified in a time- and state-dependent manner. Here we show that the resulting trajectory of the qubit in the phase space can be weakly controlled without any direct action on the qubit (control-free control), even if only one fixed observable is measured. In particular, we demonstrate a possibility of a weak form of a stochastic ratchet, allowing us to weakly push the qubit's state without any net force in the effective potential. Furthermore, if the weak measurement strength is significantly reduced in a way conditioned to some particular state, a dynamical localization near this state takes place. If the measurement strength is reduced to zero, a singularity appears, which behaves like an artificial basis state.

Various classical models of electrons including their spin degrees of freedom are commonly applied to describe the electron dynamics in strong electromagnetic fields. We demonstrate that different models can lead to different or even contradicting predictions regarding how the spin degree of freedom modifies the electron's orbital motion when the electron moves in strong electromagnetic fields. This discrepancy is rooted in the model-specific energy dependency of the spin-induced Stern-Gerlach force acting on the electron. The Frenkel model and the classical Foldy-Wouthuysen model are compared exemplarily in the nonrelativistic and the relativistic limits in order to identify parameter regimes where these classical models make different predictions. This allows for experimental tests of these models. In ultrastrong laser setups in parameter regimes where effects of the Stern-Gerlach force become relevant, radiation-reaction effects are also expected to set in. We incorporate the radiation reaction classically via the Landau-Lifshitz equation and demonstrate that although radiation-reaction effects can have a significant effect on the electron trajectory, the Frenkel model and the classical Foldy-Wouthuysen model remain distinguishable also if radiation-reaction effects are taken into account. Our calculations are also suitable to verify the Landau-Lifshitz equation for the radiation reaction of electrons and other spin-1/2 particles.

The differential-phase-shift (DPS) quantum-key-distribution (QKD) protocol was proposed aiming at simple implementation, but it can tolerate only a small disturbance in a quantum channel. The round-robin DPS (RRDPS) protocol could be a good solution for this problem, which in fact can tolerate even up to $50\%$ of a bit error rate. Unfortunately, however, such a high tolerance can be achieved only when we compromise the simplicity, i.e., Bob's measurement must involve a large number of random delays ($\left|\mathcal{R}\right|$ denotes its number), and in a practical regime of $\left|\mathcal{R}\right|$ being small, the tolerance is low. In this paper, we propose a DPS protocol to achieve a higher tolerance than the one in the original DPS protocol, in which the measurement setup is less demanding than the one of the RRDPS protocol for the high tolerance regime. We call our protocol the small-number-random DPS (SNRDPS) protocol, and in this protocol, we add only a small amount of randomness to the original DPS protocol, i.e., $2\le \left|\mathcal{R}\right|\le 10$. In fact, we found that the performance of the SNRDPS protocol is significantly enhanced over the original DPS protocol only by employing a few additional delays such as $\left|\mathcal{R}\right|=2$. Also, we found that the key generation rate of the SNRDPS protocol outperforms the RRDPS protocol without monitoring the bit error rate when it is less than $5\%$ and $\left|\mathcal{R}\right|\le 10$. Our protocol is an intermediate protocol between the original DPS protocol and the RRDPS protocol, and it increases the variety of the DPS-type protocols with quantified security.

Magnetically tunable Feshbach resonances are an indispensable tool for experiments with atomic quantum gases. We report on 37 thus far unpublished Feshbach resonances and four further probable Feshbach resonances in spin mixtures of ultracold fermionic ${}^{40}\mathrm{K}$ with temperatures well below 100 nK. In particular, we locate a broad resonance at $B=389.7\text{G}$ with a magnetic width of $26.7\text{G}$. Here $1\text{G}={10}^{-4}\text{T}$. Furthermore, by exciting low-energy spin waves, we demonstrate a means to precisely determine the zero crossing of the scattering length for this broad Feshbach resonance. Our findings allow for further tunability in experiments with ultracold ${}^{40}\mathrm{K}$ quantum gases.

The dynamics of the Mie plasmon is described in the framework of the self-consistent quantum Vlasov theory by a reduced single-state model. The single-state model is validated by many-electron calculations for Na clusters. In this framework, collisionless damping of the Mie plasmon can be investigated for a wide range of cluster parameters by linear perturbation theory. The characteristic scaling of the damping rate with the inverse cluster radius is demonstrated. The basic damping mechanism of the Mie plasmon can be explained by a conversion of surface modes into volume modes due to the scattering by the self-consistent potential of the electron-electron interaction at the cluster boundary.

An interacting cigar-shaped Bose-Einstein condensate (BEC) inside a driven optical cavity exhibits an intrinsic cross-Kerr (CK) nonlinearity due to the interaction with the optical mode of the cavity. Although the CK coupling is much weaker than those of the radiation pressure and the atom-atom interactions, it can affect the bistability behavior of the system when the intensity of the laser pump is strong enough. On the other hand, there is a competition between the CK nonlinearity and the atom-atom interaction so that the latter can neutralize the effect of the former. Furthermore, the CK nonlinearity causes the effective frequency of the Bogoliubov mode of the BEC as well as the quantum fluctuations of the system to be increased by increasing the cavity driving rate. However, in the dispersive interaction regime the effect of the CK nonlinearity is negligible. In addition, we show that by increasing the $s$-wave scattering frequency of atomic collisions one can generate a strong stationary quadrature squeezing in the Bogoliubov mode of the BEC.

Scattering is a general process in both fundamental and applied physics. In this paper, we investigate Rayleigh scattering of a solid-state-emitter coupled to a nanofiber, by $S$-matrix-like theory in $k$-space description. Under this model, both Rayleigh scattering and dipole interaction are studied between a two-level artificial atom embedded in a nanocrystal and fiber modes (guided and radiation modes). It is found that Rayleigh scattering plays a critical role in the transport properties and quantum statistics of photons. On the one hand, Rayleigh scattering produces the transparency in the optical transmitted field of the nanofiber, accompanied by the change of atomic phase, population, and frequency shift. On the other hand, the interference between two kinds of scattering fields by Rayleigh scattering and dipole transition modifies the photon statistics (second-order autocorrelation function) of output fields, showing a strong wavelength dependence. This study provides guidance for the solid-state emitter acting as a single-photon source and can be extended to explore the scattering effect in many-body physics.

We consider a generalized modular-value-based scheme based on the standard von Neumann measurement. We model the scheme as an interaction between a quantum system and a discrete quantum pointer where the pointer operator is a projection operator onto one of the states of the basis of the pointer Hilbert space. The interaction strength is made arbitrarily large. After post-selection onto the system, the results of the pointer measurement are the so-called conditional probabilities. We first explicitly derive the analytical expressions of the conditional probabilities, the expectation value, and the average displacement in the measured value of a pointer observable that we name as the pointer quantities. We also provide an expression for a generalized modular value and discuss the relationship between the generalized modular value and generalized weak values. The study then shows that the generalized modular value can characterize these pointer quantities. Then we give applications of our proposal to the cases of a spin-$s$ particle pointer and a semiclassical pointer state. One of the key results is that the amplification effect, similar to the weak-value case, is also observed in the case of the generalized modular value. Our study can also apply to the cases of nonclassical pointer states.

We consider quantum circuits with time travel designed for distinguishing specific nonorthogonal quantum states in two of the most popular models: Deutsch's and postselected. We modify them by the presence of a weakly coupled thermal environment. Using the Davies approximation, we study how the thermal noise affects the ability of circuits to distinguish nonorthogonal quantum states. We show that for a purely dephasing environment the paradoxical power of such circuits remains preserved. We also present a physics-based argument for conditions of validity of the maximum-entropy rule introduced by Deutsch for resolving the uniqueness ambiguity in a circuit with time travel.

We provide an example of a communication model and a distributed task, for which there exists a realistic quantum protocol that is asymptotically more efficient than any classical protocol, both in the communication and the information resources. For this, we extend a recently proposed coherent state mapping for quantum communication protocols, study the use of coherent state fingerprints over multiple channels, and show their role in the design of an efficient quantum protocol for estimating the Euclidean distance of two real vectors within a constant factor.

Leading approaches to fault-tolerant quantum computation dedicate a significant portion of the hardware to computational factories that churn out high-fidelity ancillas called magic states. Consequently, efficient and realistic factory design is of paramount importance. Here we present the most detailed resource assessment to date of magic-state factories within a surface code quantum computer, along the way introducing a number of techniques. We show that the block codes of Bravyi and Haah [Phys. Rev. A 86, 052329 (2012)] have been systematically undervalued; we track correlated errors both numerically and analytically, providing fidelity estimates without appeal to the union bound. We also introduce a subsystem code realization of these protocols with constant time and low ancilla cost. Additionally, we confirm that magic-state factories have space-time costs that scale as a constant factor of surface code costs. We find that the magic-state factory required for postclassical factoring can be as small as 6.3 million data qubits, ignoring ancilla qubits, assuming ${10}^{-4}$ error gates and the availability of long-range interactions.

Stabilizer states are extensively studied in quantum information theory for their structures based on the Pauli group. Calderbank-Shor-Steane (CSS) stabilizer states are of particular importance in their application to fault-tolerant quantum computation (FTQC). However, how to fault-tolerantly prepare arbitrary CSS stabilizer states for general CSS stabilizer codes is still unknown, and their preparation can be highly costly in computational resources. In this paper, we show how to prepare a large class of CSS stabilizer states useful for FTQC. We propose distillation protocols using syndrome encoding by classical codes or quantum CSS codes. Along the same lines, we show that classical coding techniques can reduce the ancilla consumption in Steane syndrome extraction by using additional transversal controlled-not gates and classical computing power. In the scenario of a fixed ancilla consumption rate, we can increase the frequency of quantum error correction and effectively lower the error rate.

Entanglement, a unique quantum resource with no classical counterpart, remains at the heart of quantum information. The Greenberger-Horne-Zeilinger (GHZ) and $W$ states are two inequivalent classes of multipartite entangled states which cannot be transformed into each other by means of local operations and classic communication. In this paper, we present the methods to prepare the GHZ and $W$ states via global controls on a long-range Ising spin model. For the GHZ state, general solutions are analytically obtained for an arbitrary-size spin system, while for the $W$ state, we find a standard way to prepare the $W$ state that is analytically illustrated in three- and four-spin systems and numerically demonstrated for larger-size systems. The number of parameters required in the numerical search increases only linearly with the size of the system.

A feedback control method for producing an equidistant ion string in a surface-electrode ion trap has been experimentally demonstrated. This method features three advantages: (i) The optimal voltage can be constrained within the specified reachable range. (ii) The height of trapped ions from the trap surface can be maintained at the same value when strings with different number of ions or with different ion spacings are to be trapped. (iii) This method is resistant to a stray electric field near the trap. By this method, the asymmetry of the ion string caused by a stray field is minimized. The robustness of trapping a variable number of ions at the same potential and the dependency of the axial frequency on the number of ions are also investigated experimentally. This work would be a practical method to create a linear ion string with a large number of ions and may find applications in large-scale quantum computing, quantum simulation, and phase transition studies utilizing homogeneous ion strings.

Spin-exchange optical hyperpolarization of ${}^{129}\mathrm{Xe}$ gas enhances the signal-to-noise ratio in nuclear magnetic resonance experiments. The governing parameter of the Rb-Xe spin-exchange process, the so-called enhancement factor, was recently reevaluated experimentally. However, the underlying hyperfine coupling and atomic interaction potential as functions of the internuclear distance of the open-shell Rb-Xe dimer have not been accurately determined to date. We present a piecewise approximation based on first-principles calculations of these parameters contributing to the NMR and EPR frequency shifts in the low-density Rb-Xe gas mixture of relevance to hyperpolarization experiments. Both Rb electron and ${}^{129}\mathrm{Xe}$ nuclear spin polarizations are estimated based on a combination of electronic-structure calculations, observed frequency shifts, and an estimate of the Rb number density. Finally, an expression for the enhancement factor in terms of modern electronic-structure theory is obtained.

We consider the basic collision dynamics of single ionization of helium by 1-MeV protons using distorted-wave models and the first Born approximation. A good agreement is found between results of the distorted-wave models and recent experimental data [H. Gassert, O. Chuluunbaatar, M. Waitz et al., Phys. Rev. Lett. 116, 073201 (2016)] for electron emission into the azimuthal plane. However, unexpected discrepancies are observed between the theoretical results and the experimental data for the emission into the collision plane. Our consideration also shows that even though these collisions belong to the regime of weak perturbations, substantial differences exist between the results of the distorted-wave models and the first Born approximation.

We investigate the energy dependence and the internal-state dependence of the charge-exchange collision cross sections in a mixture of ${}^6\mathrm{Li}$ atoms and ${{}^{40}\mathrm{Ca}}^{+}$ ions. Deliberately excited ion micromotion is used to control collision energy of atoms and ions. The energy dependence of the charge-exchange collision cross section obeys the Langevin model in the temperature range of the current experiment, and the measured magnitude of the cross section is correlated to the internal state of the ${{}^{40}\mathrm{Ca}}^{+}$ ions. Revealing the relationship between the charge-exchange collision cross sections and the interaction potentials is an important step toward the realization of the full quantum control of the chemical reactions at an ultralow-temperature regime.

We study inelastic two-body relaxation in a spin-polarized ultracold Fermi gas in the presence of a $p$-wave Feshbach resonance. It is shown that in reduced dimensionalities, especially in the quasi-one-dimensional case, the enhancement of the inelastic rate constant on approach to the resonance is strongly suppressed compared to three dimensions. This may open promising paths for obtaining novel many-body states.

We theoretically analyze angle-resolved photoelectron spectra (ARPES) generated by the interaction of ${\text{C}}_{60}$ with intense, short laser pulses. In particular, we focus on the impact of the carrier-envelope phase (CEP) onto the angular distribution. The electronic dynamics is described by time-dependent density functional theory, and the ionic background of ${\text{C}}_{60}$ is approximated by a particularly designed jellium model. Our results show a clear dependence of the angular distributions onto the CEP for very short pulses covering only very few laser cycles, which disappears for longer pulses. For the specific laser parameters used in recent experiments, a very good agreement is obtained. Furthermore, the asymmetry is found to depend on the energy of the emitted photoelectrons. The strong influence of the angular asymmetry of electron emission onto the CEP and pulse duration suggests using this sensitivity as a means to analyze the structure of few-cycle laser pulses.