In this paper, we present a realization of an on chip atomic clock using a cold cloud of ${}^{87}\mathrm{Rb}$ atoms. This clock is based on a Ramsey interferometer with a Ramsey time around 600 ms. This is realized with large laboratory temperature drift during the measurement (few degrees per day) and without magnetic-field shielding. We review the experimental implementation of this clock and give a full study of the known noises present in this atomic clock.

The effective frequency of a mechanical resonator can be tuned via the spring effect induced by quadratic optomechanical (QOM) coupling, and both spontaneous symmetry breaking and anti-parity-time phase transition were predicted in the QOM systems. Here, we show that the mechanical susceptibility can be enhanced significantly by driving the QOM system with a strong external optical field, and divergence will happen as the driving strength approaches the critical point (CP) for spontaneous symmetry breaking. Based on the CP, we propose a highly sensitive temperature sensor with a mechanical resonator quadratically coupled to an optical mode. We find that the sensitivity of the temperature sensor can be enhanced by several orders of magnitude as the driving strength approaches the CP, and the sensitivity of the temperature sensor remains high in the low-temperature limit. Our work provides an effective way to realize highly sensitive temperature sensing at ultralow temperature in QOM systems.

We derive Bethe's formula for the Lamb shift by extending Feynman's suggestion that the shift could be interpreted as the change, due to the presence of the atom, in electromagnetic field energy. This approach is based on measurable quantities such as a refractive index but has a contribution from virtual photon absorption which is effectively eliminated by a high-energy cutoff in the nonrelativistic theory. We show that this unphysical contribution is canceled when a self-interaction energy is included in Feynman's argument.

Correlations, as intrinsic and intriguing features of quantum systems, have profound implications and applications in quantum information theory. Although substantial progress has been made in understanding and applying spatial correlations (i.e., those across different spatial systems at the same instant of time), temporal correlations (which emerge from the dynamics of a single quantum system across different instants of time) have been relatively less investigated. In this work, we first provide an axiomatic approach to temporal correlations by postulating natural requirements for a reasonable monotone of temporal correlations generated by a quantum channel. Then we study the temporal correlating power of quantum channels in terms of the Jordan product of quantum channels and compare it with the recently introduced notion of state over time. We introduce an information-theoretic monotone of such a power by exploiting the Jordan negativity and reveal its basic properties such as convexity, monotonicity, and unitary invariance. We further illustrate the monotone through several important channels and explicitly evaluate the corresponding temporal correlating power.

We compare four different encoding schemes for the quantum computing of spin chains with a spin quantum number $S>1/2$: a compact mapping, a direct (or one-hot) mapping, a Dicke mapping, and a qudit mapping. The three different qubit encoding schemes are assessed by conducting a Hamiltonian simulation for $1/2\le S\le 5/2$ using a trapped-ion quantum computer. The qudit mapping is tested by running simulations with a simple noise model. The Dicke mapping, in which the spin states are encoded as superpositions of multiqubit states, is found to be the most efficient because of the small number of terms in the qubit Hamiltonian. We also investigate the $S$ dependence of the time step length $\mathrm{\Delta }\tau$ in the Suzuki-Trotter approximation and find that $\mathrm{\Delta }\tau$ should be inversely proportional to $S$ in order to obtain the same accuracy for all $S$.

We extend the controlled displacement interaction between a qubit and a harmonic oscillator to the multiqubit (qudit) case. We define discrete quadratures of the qudit and show how the qudit state can be displaced in these quadratures controlled by an oscillator quadrature. Using this interaction, a periodic repetition of the state encoded in the qudit, can be deterministically mapped onto the oscillator, which is initialized in a squeezed state. Based on this controlled displacement interaction, we present a full circuit that encodes quantum information in a superposition of qudit quadrature states, and successively prepares the oscillator in the corresponding superposition of approximate Gottesman-Kitaev-Preskill (GKP) states. This preparation scheme is found to be similar to phase estimation, with the addition of a disentanglement gate. Our protocol for GKP state preparation is efficient in the sense, that the set of qubits need only interact with the oscillator through two time-independent interactions, and in the sense that the squeeze factor (in dB) of the produced GKP state grows linearly in the number of qubits used.

The production of the projectile $2s2p{}^{3}P$ and $2s2p{}^{1}P$ autoionizing states is investigated in 0.5–1.5 MeV/u collisions of He-like carbon and oxygen mixed-state three-component $(1s^2,1s2s{}^{3}S,1s2s{}^{1}S)$ ion beams with helium targets. The mixed-state beams are produced in the stripping systems of the 5.5-MV Demokritos tandem accelerator. Using high-resolution Auger projectile electron spectroscopy, the normalized Auger electron yields are measured at $0^{\circ }$ relative to the beam direction. In addition, a three-electron atomic orbital close-coupling approach, employing full configuration interaction and antisymmetrization of the three-electron, two-center total wave function, is applied to calculate the production cross sections for these states from each of the three initial ion beam components. Thereupon, the theoretical Auger yields are computed and found to be mostly smaller than experiment by factors ranging from near 1 to about 10. Agreement, however, improves when larger $1s2s{}^{1}S$ fractions, not only based on spin statistics, are projected. Overall, we present a careful and sophisticated analysis with a thorough discussion of these results which show that our current understanding is still incomplete. Nevertheless, our nonperturbative excitation treatment—free from scaling parameters and renormalization—marks a significant advancement in modeling ultrafast multielectron dynamics within open-shell quantum systems.

Hollow-core photonic crystal fibers (HC-PCFs) are a highly appealing tool for the optical trapping of micron-sized dielectric probes. Indeed, controlling the optical modes of HC-PCFs through diffractive spatial light modulators might lead to generate specific and accurate three-dimensional traps. Here, optical traps suitable for controlling dielectric nano- and microspheres using near-infrared wavelengths inside a HC-PCF are analyzed in depth, through a generalized Lorenz-Mie theory approach. The method provides an accurate and enhanced description of versatile trapping configurations, including optical conveyor belts. The applications of these trapping techniques can be various and important, including the development of optical sensors based on the light-matter interaction in the core.

Optical force can enable precise manipulations of small particles for various applications. It is well known that an isotropic lossless dielectric sphere is only subject to forward optical force under the illumination of an electromagnetic plane wave. By using rigorous full-wave simulations, we show that such a sphere can experience a lateral optical force and an optical torque besides the conventional longitudinal force, if it spins with a constant angular velocity. The emergence of the unusual optical force and torque is attributed to the breaking of mirror and cylindrical symmetries by the spinning motion. Using the multipole expansion in source representation, we illustrate how the spinning-induced effective bianisotropy generates the lateral force and torque on the sphere through the interference of electric and magnetic multipoles. We also uncover the effect of Sagnac frequency splitting on the optical force and torque. The results contribute to the understanding of the optical force and torque in moving media and can be applied to realize unconventional optical manipulations of small particles.

Quantum coherence in bosonic systems is a fundamental resource for quantum technology applications. In this work, we introduce a framework for analyzing coherence in the Fock-state basis, utilizing context-dependent certification to reveal the quantum non-Gaussian nature of the tested coherence. Rather than relying on global coherence measures, our approach targets specific aspects of coherence, enabling a tailored hierarchical classification. We derive and compare two distinct hierarchies, each representing a different context for coherence in bosonic systems. Motivated by current advancements in optical quantum state engineering, we assess the feasibility and depth of these hierarchies under conditions of loss and thermal noise. The methodology introduced here is versatile and can be extended to multistate and multimode coherences, making it adaptable to a wide range of experimental scenarios and platforms.

The uncertainty principle is one of the fundamental principles of quantum mechanics. Exploring such uncertainty relations in pre- and postselected (PPS) systems, where weak measurements on postselected states have been used as a powerful tool for exploring the foundation of quantum mechanics, has so far eluded experimental effort. In this work, we experimentally investigate the Robertson-Heisenberg-type uncertainty relation for two incompatible observables in a PPS system. Through conducting a von Neumann-type measurement, uncertainty relations between two noncommuting Pauli observables are experimentally unveiled. Such uncertainty relations in the PPS system impose limitations on the joint sharp preparation of pre- and postselected states for two incompatible observables. Our experiments would be useful for the development of amplification techniques for precision measurements.

Trends of genuine entanglement in Haar uniformly generated multimode pure Gaussian states with fixed average energy per mode are explored. A distance-based metric known as the generalized geometric measure (GGM) is used to quantify genuine entanglement. The GGM of a state is defined as its minimum distance from the set of all nongenuinely entangled states. To begin with, we derive an expression for the Haar-averaged value of any function defined on the set of energy-constrained states. Subsequently, we investigate states with a large number of modes and provide a closed-form expression for the Haar-averaged GGM in terms of the average energy per mode. Furthermore, we demonstrate that typical states closely approximate their Haar-averaged GGM value, with deviation probabilities bounded by an exponentially suppressed limit. We then analyze the GGM content of typical states with a finite number of modes and present the distribution of GGM. Our findings indicate that, as the number of modes increases, the distribution shifts towards higher entanglement values and becomes more concentrated. We quantify these features by computing the Haar-averaged GGM and the standard deviation of the GGM distribution, revealing that the former increases while the latter decreases with the number of modes. Finally, we compare the typical value of the GGM with its maximal value consistent with the imposed energy bound.

We theoretically propose a circuit of the four-body coupler for superconducting qubits based on Josephson parametric oscillators (JPOs). Our coupler for the four-body interaction has a superconducting loop, similar to a capacitively shunted flux qubit, where an external magnetic flux set to half a flux quantum is threaded. This coupler circuit is a specific setup of the circuit called superconducting nonlinear asymmetric inductive elements (SNAIL) and also is a generalization of the previously proposed one for the four-body interaction of JPOs. We clarify roles of circuit parameters in the four-body interaction and, in particular, show that the four-body coupling constant in our circuit can be significantly increased by tuning capacitance of the coupler or the area ratio of the Josephson junctions of the coupler.

We report the measurement of the electric dipole moment of aluminum monochloride (AlCl) using a cryogenic buffer-gas beam source. Using Stark shift spectroscopy, we derive values for the dipole moments in the body-fixed frame of the two lowest vibrational states for the $X^1{\mathrm{\Sigma }}^{+}$ electronic state, ${\mu }_X(v^{\prime \prime }=0)=-1.679$ D and ${\mu }_X(v^{\prime \prime }=1)=-1.761$ D, and for the $A^1\mathrm{\Pi }$ state, ${\mu }_A(v^{\prime }=0)=-1.030$ D and ${\mu }_A(v^{\prime }=1)=-1.052$ D. We also show that the ab initio calculations of the dipole moment and $T_e$ energy of AlCl are sensitive to the level of treatment of the spin-orbit orbit coupling. We further lay out the implications of these results for astrophysical models of stellar and planetary evolution that have used a substitute value for the dipole moment of AlCl until now.

We investigate a system of bosons in a two-dimensional harmonic trap. In the limit of strong attractive interactions, the bosons make a droplet insensitive to external confinement. For weak interactions, in contrast, the ground state is given by the harmonic trap. In this work, we conduct a variational study of the transition between these two limits. We find that this transition occurs at the critical interaction strength whose value is universal if scaled appropriately with the number of particles. To connect the change in the properties of the system to the classical description of phase transitions, we analyze the static response of the Bose gas related to the isothermal compressibility. Finally, we perform numerically exact calculations for a few particles to demonstrate the effects of finite-range interactions on this transition. We conclude that finite-range effects wash out the point of transition.

The quantum approximate optimization algorithm, also known in its generalization as the quantum alternating operator ansatz, (QAOA) is a heuristic hybrid quantum-classical algorithm for finding high-quality approximate solutions to combinatorial optimization problems, such as maximum satisfiability. While the QAOA is well studied, theoretical results as to its runtime or approximation ratio guarantees are still relatively sparse. We provide some of the first lower bounds for the number of rounds (the dominant component of QAOA runtimes) required for the QAOA. For our main result, we (i) leverage a connection between quantum annealing times and the angles of the QAOA to derive a lower bound on the number of rounds of the QAOA with respect to the guaranteed approximation ratio. We apply and calculate this bound with Grover-style mixing unitaries and (ii) show that this type of QAOA requires at least a polynomial number of rounds to guarantee any constant approximation ratios for most problems. We also (iii) show that the bound depends only on the statistical values of the objective functions and, when the problem can be modeled as a $k$-local Hamiltonian, can be easily estimated from the coefficients of the Hamiltonians. For the conventional transverse-field mixer, (iv) our framework gives a trivial lower bound to all bounded-occurrence local cost problems and for all strictly $k$-local cost Hamiltonians matching known results that constant approximation ratio is obtainable with a constant-round QAOA for a few optimization problems from these classes. Using our proof framework, (v) we recover the Grover lower bound for unstructured search and, with small modification, show that our bound applies to any QAOA-style search protocol that starts in the ground state of the mixing unitaries.