A parametric amplifier is in essence a linear four-port device, which couples and linearly mixes two inputs before amplifying and sending them to two output ports. Here we show that for quadrature-phase amplitudes, a parametric amplifier can replace beam splitters to play the role of the mixer. We apply this idea to a continuous-variable quantum state teleportation scheme in which a parametric amplifier replaces a beam splitter in the Bell measurement. We show that this scheme is loss tolerant in the Bell measurement process and thus demonstrate the advantage of the parametric amplifier over the beam splitter in the applications in quantum measurement.

The Gottesman-Kitaev-Preskill (gkp) quantum error-correcting code attracts much attention in continuous variable (CV) quantum computation and CV quantum communication due to the simplicity of error-correcting routines and the high tolerance against Gaussian errors. Since the gkp code state should be regarded as a limit of physically meaningful approximate ones, various approximations have been developed until today, but explicit relations among them are still unclear. In this paper, we rigorously prove the equivalence of these approximate gkp codes with an explicit correspondence of the parameters. We also propose a standard form of the approximate code states in the position representation, which enables us to derive closed-form expressions for the Wigner function, inner products, and the average photon number in terms of the theta functions. Our results serve as fundamental tools for further analyses of fault-tolerant quantum computation and channel coding using approximate gkp codes.

Based on the fundamental momentum-transfer theorem [B. A. Lippmann, Phys. Rev. Lett. 15, 11 (1965)], a contribution to the retarding force of metallic systems for slow intruders is derived. This contribution is associated with sudden charge-changing cycles during the path of projectiles. The sum of this and the well-known conventional contributions, both expressed in terms of scattering phase shifts, is used to discuss experimental data obtained for different targets. It is found that our two-channel modeling, with two nonlinear channels, improves the agreement between data and theory and thus, as predictive modeling, can contribute to the desired convergence between experimental and theoretical attempts at the retarding force.

A combined density and density-matrix functional method is proposed for the calculation of potential energy curves of molecular multibond dissociation. Its density-matrix part, a pair-density functional, efficiently approximates the ab initio pair density of the complete active space (CAS) method. The corresponding approximate on-top pair density $\mathrm{\Pi }$ is employed to correct for double counting in the correlation energy functional. The proposed $\mathrm{ELS}+$ method, which augments the extended Löwdin-Shull (ELS) density-matrix functional with the $\mathrm{\Pi }$-based scaled density functional, closely reproduces potential curves of the paradigmatic multibond dissociation in ${\mathrm{N}}_2, {\mathrm{H}}_2\mathrm{O}$, and ${\mathrm{H}}_2\mathrm{CO}$ molecules calculated with the recently proposed $\mathrm{CAS}\mathrm{\Pi }\mathrm{DFT}$ [CAS augmented with the $\mathrm{\Pi }$-based scaled correlation correction of density functional theory (DFT)] method. Furthermore, with the additional correction for the intrafragment correlation between the broken-bond electrons, $\mathrm{ELS}++$ reproduces well the benchmark potential curve of the ${\mathrm{N}}_2$ molecule by Lie and Clementi.

We study the decay of bosonic many-body states in the triple-well Bose-Hubbard model where bosons in the central well can escape into a reservoir. For vanishing interparticle interaction this system supports a nondecaying many-body state which is the antisymmetric Bose-Einstein condensate with particles occupying only the edge wells. In the classical approach this quantum state corresponds to a symmetry-protected nondecaying state which is stable even at finite interaction below a certain intensity threshold. Here we demonstrate that despite the fact that the classical counterpart is stable the antisymmetric Bose-Einstein condensate is always metastable at finite interatomic interactions due to quantum fluctuations.

Precision spectroscopy of ${\mathrm{Li}}^{+}$ is a promising testing ground for bound-state quantum electrodynamics (QED) and for measurements of nuclear properties such as the Zemach radius. We investigate the hyperfine and fine-structure splittings of the $2{}^{3}S_1$ and $2{}^3{P}_J$ states of ${}^7\mathrm{Li}^{+}$ using saturated fluorescence spectroscopy based on a $\sim 460\mathrm{eV}$ metastable ion beam. We measure in particular the $2{}^{3}S_1–2{}^{3}P_J$ transitions in ${}^7\mathrm{Li}^{+}$. With a triple nested loop scanning method, the long-term drift and systematic uncertainties are reduced or eliminated, resulting in a total uncertainty of less than 100 kHz. Our results are in good agreement with QED calculations. For the hyperfine splittings of $2{}^{3}S_1$, our measured values have a similar accuracy to previous measurements and theoretical calculations. For the $2{}^3{P}_J$ fine and hyperfine splittings, our measured results are one order of magnitude more accurate than those of previous measurements and have a similar accuracy to the theoretical values. The measurements lay the foundation for future work on the ${\mathrm{Li}}^{+}$ isotopes and their theoretical interpretation in terms of nuclear charge radii and the Zemach radii.

Adiabatic elimination methods allow the reduction of the space dimension needed to describe systems whose dynamics exhibit separation of timescale. For open quantum systems, it consists in eliminating the fast part assuming it has almost instantaneously reached its steady state and obtaining an approximation of the evolution of the slow part. These methods can be applied to eliminate a linear subspace within the system Hilbert space or, alternatively, to eliminate a fast subsystem in a bipartite quantum system. In this work, we extend an adiabatic elimination method used for removing fast degrees of freedom within a system [Phys. Rev. A 101, 042102 (2020)] to eliminate a subsystem from an open bipartite quantum system. As an illustration, we apply our technique to a dispersively coupled two-qubit system and in the case of the open Rabi model.

It is known that the dynamics and geometric phase of a quantum system could be mapped mathematically into a classical system of coupled oscillators without loss of physics. In this work, we show that this quantum-classical mapping can also be used to simulate non-Abelian dynamics and phase of the quantum system with energy degeneracy by interpreting the quantum degeneracy as the resonance between the eigenfrequencies of the classical oscillators. The quantum evolution and Wilczek-Zee phase in the degenerate subspace can also be described by the classical non-Abelian evolution and a non-Abelian geometric angle in the resonant subspace. By studying the adiabatic evolution in this classical non-Abelian case, our results can also be used to generalize the concept of averaging principle and Hannay's angle into the classical system with resonant eigenfrequencies. The quantum-classical mapping of a tripod-scheme Hamiltonian with two degenerate dark states is employed to illustrate the classical non-Abelian dynamics and geometric angles.

One of the most important algorithmic applications of quantum walks is to solve spatial search problems. A widely used quantum algorithm for this problem, introduced by Childs and Goldstone [Phys. Rev. A 70, 022314 (2004)], finds a marked node on a graph of $n$ nodes via a continuous-time quantum walk. This algorithm is said to be optimal if it can find any of the nodes in $O\left(\sqrt{n}\right)$ time. However, given a graph, no general conditions for the optimality of the algorithm are known and previous works demonstrating optimal quantum search for certain graphs required an instance-specific analysis. In fact, the demonstration of the necessary and sufficient conditions that a graph must fulfill for quantum search to be optimal has been a long-standing open problem. In this work we make significant progress towards solving this problem. We derive general expressions, depending on the spectral properties of the Hamiltonian driving the walk, that predict the performance of this quantum search algorithm provided certain spectral conditions are fulfilled. Our predictions are valid, for example, for (normalized) Hamiltonians whose spectral gap is considerably larger than $n^{-1/2}$. This allows us to derive necessary and sufficient conditions for optimal quantum search in this regime, as well as provide examples of graphs where quantum search is suboptimal. In addition, by extending this analysis, we are also able to show the optimality of quantum search for certain graphs with very small spectral gaps, such as graphs that can be efficiently partitioned into clusters. Our results imply that, to the best of our knowledge, all prior results analytically demonstrating the optimality of this algorithm for specific graphs can be recovered from our general results.

We investigate two schemes for generating indistinguishable single photons, a key feature of quantum networks, from a trapped ion coupled to an optical cavity. Through selection of the initial state in a cavity-assisted Raman transition, we suppress the detrimental effects of spontaneous emission on the photon's coherence length, measuring a visibility of $81\left(2\right)\%$ without subtraction of background counts in a Hong-Ou-Mandel interference measurement, the highest reported for an ion-cavity system. In comparison, a visibility of 50(2)% was measured using a more conventional single-photon scheme. We demonstrate through numerical analysis of the single-photon generation process that our scheme produces photons of a given indistinguishability with a greater efficiency than the conventional one. Single-photon schemes such as the one demonstrated here have applications in distributed quantum computing and communications, which rely on high-fidelity entanglement swapping and state transfer through indistinguishable single photons.

The stopping power and straggling of backscattered protons on nanometric Pt films were measured at low to medium energies (60–250 keV) by using the medium-energy ion scattering technique. The stopping power results are in good agreement with the most recent measurements by Primetzhofer Phys. Rev. B 86, 094102 (2012) and are well described by the free electron gas model at low projectile energies. Nevertheless, the straggling results are strongly underestimated by well-established formulas up to a factor of two. Alternatively, we propose a model for the energy-loss straggling that takes into account the inhomogeneous electron-gas response, based on the electron-loss function of the material, along with bunching effects. This approach yields remarkable agreement with the experimental data, indicating that the observed enhancement in energy-loss straggling is due to bunching effects in an inhomogeneous electron system. Nonlinear effects are of minor importance for the energy-loss straggling.

Spin-exchange optical pumping (SEOP) enables hyperpolarization of magnetic noble gas nuclei and allows enormously enhanced signal in nuclear magnetic resonance studies in materials, biosciences, and medicine. We model the dynamics of the SEOP process taking place in a $\mathrm{Rb}-{}^{129}\mathrm{Xe}$ gas mixture and shed light on how the different microscopic processes influence the macroscopic polarization transfer. For each Rb-Xe collision taking place in simulated molecular dynamics trajectory, we sample a time series of quantum-chemically preparametrized Hamiltonians. Combined electron and nuclear spin dynamics of each event is propagated by solving the corresponding Liouville–von Neumann equation. The rarely occurring, long-lived van der Waals molecules are seen to give the most significant contribution to polarization transfer under the simulated conditions ($T=300$ K, $p=2.4$ bar), in agreement with earlier findings. Besides the lifetime of the collision complex, the average and minimum Rb-Xe interatomic distances characterize the efficiency of the polarization transfer events. We obtain insight into magnetization transfer in both individual binary collisions and van der Waals complexes and demonstrate a stepwise buildup of ${}^{129}\mathrm{Xe}$ spin polarization upon bond-length oscillations in the latter.

We systematically investigate the interference of nuclear wave packets carrying different angular momenta by numerically solving the time-dependent Schrödinger equation for the dissociation of ${{\mathrm{H}}_2}^{+}$ in strong circularly polarized laser pulses. ${{\mathrm{H}}_2}^{+}$ exposed to strong laser pulses may absorb different numbers of photons and dissociate along different pathways carrying different angular momenta. In case dissociation pathways differ by an even number of photons, the respective wave packets have the same parity and thus interfere with each other, leading to spiral nuclear momentum distributions for the dissociative fragments. Inversely, by investigating the interference structure of the angle-resolved kinetic energy release of the dissociative fragments, the molecular dissociation pathways can be extracted. The spiral nuclear momentum distribution provides another approach to explore ultrafast molecular dynamics.

A Faraday-wave-like parametric instability is investigated via mean-field and Floquet analysis in immiscible binary Bose-Einstein condensates. The condensates form a so-called ball-shell structure in a two-dimensional harmonic trap. To trigger the dynamics, the scattering length of the core condensate is periodically modulated in time. We reveal that in the dynamics the interface becomes unstable towards the formation of oscillating patterns. The interface oscillates subharmonically, exhibiting an $m$-fold rotational symmetry that can be controlled by maneuvering the amplitude and the frequency of the modulation. Using Floquet analysis we are able to predict the generated interfacial tension of the mixture and derive a dispersion relation for the natural frequencies of the emergent patterns. A heteronuclear system composed of ${}^{87}\mathrm{Rb}-{}^{85}\mathrm{Rb}$ atoms can be used for the experimental realization of the phenomenon, yet our results are independent of the specifics of the employed atomic species and of the parameters such as scattering lengths and trap strengths at which the driving is applied.

We study a mean-field model for the dynamics of an interacting Bose-Einstein condensate in two-dimensional pseudorelativistic materials. This model is relatively simple but contains long-lived solutions called oscillons which are absent in simple nonrelativistic condensates. We report on a variety of scenarios including interactions between pairs of oscillons and oscillons propagating across an inhomogeneous material boundary. Hitherto, relativistic oscillons have been studied only in high-energy physics and cosmology, and their relevance has not been highlighted so far in condensed-matter physics.

We present a variational calculation of the energy of an impurity immersed in a double Fermi sea of noninteracting fermions. We show that in the strong-coupling regime, the system undergoes a first-order transition between polaronic and trimer states. Our result suggests that the smooth crossover predicted in previous literature for a superfluid background is the consequence of Cooper pairing and is absent in a normal system.

Rosen-Zener-Stückelberg (RZS) interferometry has provided an important tool for presenting and describing the quantum coherence in many systems, especially in ultracold atomic systems. In this paper we propose a Floquet matrix method to recognize the resonances induced by destructive RZS interference of a periodically driving two-level system with a ${sin}^2$-type field. It is shown that the RZS resonances can be precisely distinguished into two classes: Regular resonance and accidental resonance. The former corresponds to the degenerate points in quasienergy spectrum and can be divided into integer resonance and half-integer resonance, while the latter is characterized by the eigenstate of a Floquet matrix with half of the components equaling to zero. We further discuss the possibility of experimentally observing these resonances. Particularly, it is found that a selective observation of different types of resonances can be realized in most cases by adjusting the time interval of periodic measurements.

We theoretically and numerically investigate the evolution of a discrete soliton in a semi-infinite linearly chirped one-dimensional nonlinear waveguide array (WA). The discrete soliton is self-accelerated inside the transversely chirped WA and emits a dynamic diffractive resonant radiation (DifRR). The radiation appears when the soliton wave number is matched with the linear radiation wave. Unlike the uniform WA, the DifRR can be excited even for zero wave number of the input soliton when the waveguide channels are chirped. The transverse modulation due to chirp conceptually imposes a linear potential which acts as a perturbation to soliton dynamics and leads to a monotonous wave-number shift of the propagating wave. Exploiting perturbative variational analysis we determine the equation of motion of the soliton wave number and use it to establish a modified phase-matching condition which takes into account the soliton wave-number shift and efficiently predicts the dynamic DifRR. A startling effect like generation of dual DifRR occurs as a result of the interplay between the self-accelerated soliton and its initial wave number. We exploit the modified phase-matching relation to understand this unique phenomenon of dual radiation and find a satisfactory agreement with numerical results in radiation wave-number calculation.

Bound states in the continuum (BICs) have some unusual properties and important applications in photonics. A periodic structure sandwiched between two homogeneous media is the most popular platform for observing BICs and realizing their applications. Existing studies on BICs assume the periodic structure has a $C_2$ rotational symmetry about the axis perpendicular to the periodic layer. It is known that all BICs turn to resonant states with finite quality factors if the periodic structure is perturbed by a generic perturbation breaking the $C_2$ symmetry, and a typical BIC continues to exist if the perturbation keeps the $C_2$ symmetry. We study how typical BICs depend on generic structural parameters. For a class of BICs with one opening radiation channel, we show that in the plane of two generic parameters, the BICs exist continuously as a curve. Consequently, BICs can exist on periodic structures without the $C_2$ symmetry, and they can be found by tuning a single structural parameter. The result is established analytically by a perturbation theory with two independent perturbations and validated by numerical examples. Our study reveals a much larger family for BICs on periodic structures, and provides new opportunities for future applications.

We investigated nonlinear optical processes driven by superfluorescent (SF) fields and their controllability with external laser fields. Cesium atoms were excited from the $6S$ ground state to the $8P$ state by a femtosecond laser pulse. The cascaded SF decay, $8P\to 8S\to 7P$, created coherence between the $7P$ and ground states, and led to the emission of a 455-nm pulse. A nanosecond laser pulse was applied to switch the $8S\to 7P$ transition to the $8S\to 6P$ one and newly generate an 852-nm pulse. At the same time, the nanosecond pulse suppressed the 852-nm emission through the inhibition of the development of the SF field between the $8P$ and $8S$ states, which led to the saturation of the 852-nm power with the increase of the nanosecond pulse power. The presented results offer an approach to investigate cooperative radiation processes in many-body systems and to develop an alternate light source.