We utilize two-photon, high-precision microwave spectroscopy of $ng\to (n+2)g$ transitions to precisely measure the high-angular-momentum $g$-series quantum defect of ${}^{85}\mathrm{Rb}$. Samples of cold Rydberg atoms in the $ng$ state are prepared via a three-photon optical excitation combined with controlled electric-field mixing and probed with 40-$\mu \mathrm{s}$-long microwave interaction pulses. The leading systematic uncertainty arises from DC Stark shifts, which is addressed by a cancellation of background electric fields in all three dimensions. From our measurements and an analysis of systematic uncertainties from DC and AC Stark shifts, van der Waals interactions, and microwave frequency calibration, we obtain ${\delta }_0=0.0039990\left(21\right)$ and ${\delta }_2=-0.0202\left(21\right)$. We discuss our results in context with recent work elsewhere, as well as applications towards precision measurement.

We present a precise measurement of the rubidium ionic core polarizability. The results can be useful for interpreting experiments such as parity violation or black-body radiation shifts in atomic clocks since the ionic core electrons contribute significantly to the total electrical polarizability of rubidium. We report a dipole polarizability ${\alpha }_d$ = $9.116\left(9\right)a_0^3$ and quadrupole polarizability ${\alpha }_q$ = $38.4\left(6\right)a_0^5$ derived from microwave and radio-frequency spectroscopy measurements of Rydberg states with large angular momentum. By using a relatively low principal quantum number ($17\le n\le 19$) and high angular momentum ($4\le \ell \le 6$), systematic effects are reduced compared to previous experiments. We develop an empirical approach to account for nonadiabatic corrections to the polarizability model. The corrections have less than a 1% effect on ${\alpha }_d$ but almost double ${\alpha }_q$ from its adiabatic value, bringing it into much better agreement with theoretical values.

We present photodissociation of ultracold long-range Rydberg molecules as a tool to characterize their electronic properties. We photoassociate ${}^{39}\mathrm{K}_2 37{}^{2}P$ molecules with highly entangled electronic and nuclear spins of the two bound atoms and quantify the entanglement by projection of the molecular state onto noninteracting atoms using radio-frequency photodissociation. By comparison of experimental photodissociation rates with theoretical predictions, we further characterize the electronic and nuclear wave function of the photoassociated molecules. Based on the complete characterization of the formed long-range Rydberg molecules, we demonstrate a full hyperfine-spin flip of a free ground-state atom through the interaction with a Rydberg atom.

In a retroreflective scheme with an atom initially at rest, atomic Raman diffraction adopts some of the properties of Bragg diffraction due to additional couplings to off-resonant momenta. As a consequence, double Raman diffraction has to be performed in a Bragg-type regime, where the pulse duration is sufficiently long to suppress diffraction into spurious orders. Taking advantage of this regime, double Raman allows for resonant higher-order diffraction. We study theoretically the case of third-order diffraction and compare it to first order as well as a sequence of first-order Raman pulses giving rise to the same momentum transfer as the third-order pulse. Moreover, we demonstrate that interferometry is possible, and we investigate amplitude and contrast of a third-order double Raman Mach-Zehnder interferometer. In fact, third-order diffraction constitutes a competitive tool for the diffraction of ultracold atoms and interferometry based on large momentum transfer since it allows one to reduce the complexity of the experiment as well as the total duration of the diffraction process compared to a sequence, at the cost of higher pulse intensities.

A Hall tube with a tunable flux is an important geometry for studying quantum Hall physics, but its experimental realization in real space is still challenging. Here we propose to realize a synthetic Hall tube with tunable flux in a one-dimensional optical lattice with the synthetic ring dimension defined by atomic hyperfine states. We investigate the effects of the flux on the system topology and study its quench dynamics. Utilizing the tunable flux, we show how to realize topological charge pumping, where interesting charge flow and transport are observed in rotated spin basis. Finally, we show that the recently observed quench dynamics in a synthetic Hall tube can be explained by the random flux existing in the experiment.

We reveal an interesting phenomenon of enhanced polarization-dependent transverse deflection of scattered light on a meta-atom with bianisotropy. The relationship between the spin-dependent shift and the bianisotropy is demonstrated. Unlike the usual particle, the obvious transverse scattering can be obtained by the bianisotropy. Furthermore, the lateral optical force exerted on the bianisotropic meta-atom is inevitable due to the spin Hall effect of light. This work provides a way to achieve an enhanced spin Hall effect of light and offers a platform to study the interaction between light and meta-atom with bianisotropy.

In this paper, we present the analytical theory of attosecond-pulse formation via optical modulation of an active medium of the hydrogen-like ${\mathrm{C}}^{5+}$ plasma-based x-ray laser at 3.4 nm wavelength in the “water-window” range, taking into account a variation of the population inversion caused by radiative decay of the upper lasing states. We derive an analytical solution for the x-ray field amplified by an x-ray laser with time-dependent population inversion, which is simultaneously irradiated by a strong optical laser field, and use it to find the optimal conditions for the attosecond-pulse formation from a narrow-band seeding x-ray field. We show that the shape of pulses can be improved at the cost of reduced pulse peak intensity (i) via external attenuation of the resonant spectral component of the amplified x-ray field or (ii) by using a resonantly absorbing medium (the active medium of the x-ray laser after the change of sign of the population inversion) for the pulse formation. The results of the analytical theory are in a good agreement with the numerical solutions of the Maxwell-Bloch equations which account for the nonlinearity, as well as the amplified spontaneous emission, of the active medium. Both analytically and numerically we show the possibility to produce a train of attosecond pulses with sub-200-as duration and the peak intensity exceeding ${10}^{12}\mathrm{W}/\mathrm{c}{\mathrm{m}}^2$ at the carrier wavelength 3.4 nm in the water-window range, which makes them attractive for the biological and medical applications.

We obtain a family of simple closed-form exact solutions of the three-dimensional wave equation that are free of backward components. The solutions have no singularities and possess finite energy. They describe single-cycle and subcycle pulses. Depending on two parameters, the family yields pulses with different types of localization, in particular, focused pancakes, balls, and needles.

Multiphoton nonlinear frequency mixing effects on coherent electromagnetically induced absorption spectra of ${}^{85}\mathrm{Rb}$ atoms using two orthogonal linear polarizations of strong-coupling and weak probe beams are investigated theoretically and experimentally with respect to an applied longitudinal magnetic field and coupling powers. Herein, we confirm that at least five-photon interactions in solving density matrix equations for the $F_g=3\to F_e=4$ transition of ${}^{85}\mathrm{Rb}$ atoms are required to explain experimentally observed coherent electromagnetically induced absorption spectra when a quantum axis is selected as the propagation direction of co-propagating coupling and probe laser beams. Distinct calculated spectral differences owing to variations in the magnetic field and coupling power between three- and five-photon interactions are confirmed. The obtained asymmetrical spectral shapes match very well with those calculated from five-photon interactions considering the off-resonant $F_g=3\to F_e=2,3$ transitions. Genuine coherent spectral shapes are observed with a single laser combined with two acousto-optic modulators, wherein the spectral resolution is limited because of the decoherence rate between Zeeman sublevels in the ground state from transit-time relaxation.

We study the problem of estimating a time-dependent magnetic field by continuous optical probing of an atomic ensemble. The magnetic field is assumed to follow a stochastic Ornstein-Uhlenbeck process and it induces Larmor precession of the atomic ground-state spin, which is read out by the Faraday polarization rotation of a laser field probe. The interactions and the measurement scheme are compatible with a hybrid quantum-classical Gaussian description of the unknown magnetic field, and the atomic and field variables. This casts the joint conditional quantum dynamics and classical parameter estimation problem in the form of update formulas for the first and second moments of the classical and quantum degrees of freedom. Our hybrid quantum-classical theory is equivalent to the classical theory of Kalman filtering and to the quantum theory of Gaussian states. By reference to the classical theory of smoothing and with the quantum theory of past quantum states, we show how optical probing after time $t$ improves our estimate of the value of the magnetic field at time $t$, and we present numerical simulations that analyze and explain the improvement over the conventional filtering approach.

We propose a scheme for an ultrasensitive weak measurement system with an ultrasmall rotatory dispersion effect to measure angular rotation. Estimation of angular rotation is obtained by the shift of the center wavelength. In our scheme, we obtain a continuously adjustable coupling strength and show that our system provides a 13 times higher sensitivity of 38 840 nm/rad compared with previous work. Here we demonstrate that our scheme may offer an optimal weak value $A_w$ in practice and outperforms conventional measurements in the presence of technical noise. The precision achieved by optimized weak value amplification (WVA) is about three times higher than that of a polarimeter. Our work extends the working regime of WVA. Its simplicity and robustness clear the way for widespread use of WVA involving measurements with commercial cameras and small signals.

Radiative double-electron capture (RDEC), a process considered the inverse of double photoionization of ions, has been investigated for $\sim 2$ MeV/u fully stripped and one-electron oxygen and fluorine ions colliding with thin-foil C targets. These measurements are a follow-up to the first evidence for RDEC [A. Simon, A. Warczak, T. Elkafrawy, and J. A. Tanis, Phys. Rev. Lett. 104, 123001 (2010)] in ion collisions with carbon, and to our recent observation of the process for 2.11 MeV/u ${\mathrm{F}}^{9,8+}$ ions [D. S. La Mantia, P. N. S. Kumara, S. L. Buglione, C. P. McCoy, C. J. Taylor, J. S. White, A. Kayani, and J. A. Tanis, Phys. Rev. Lett. 124, 133401 (2020)] in collisions with gas targets of ${\mathrm{N}}_2$ and Ne. Coincidences between emitted photons and outgoing ions in charge states q-2 (the expected RDEC charge state), q-1, and q were recorded. Differences in coincidences with all three charge states are appreciable and are attributed to unavoidable multiple charge-changing collisions of the ions as they transverse the thin-foil target. Also, significant differences between the spectra for oxygen and fluorine are seen, despite these ions being just one atomic number apart. Cross sections for RDEC were determined and compared with previous data for thin-foil solid and gas targets as well as with theoretical calculations.

We have observed Bloch oscillations of a ${}^4{\text{He}}^{*}$ Bose-Einstein condensate in an optical lattice at 1557.3 nm. Due to its low mass, metastable helium was efficiently accelerated orders of magnitude faster than demonstrated with other atoms. In a horizontal lattice, we could transfer a total of $800\hslash k$ of momentum by shuttling the atomic cloud back and forth 50 times between the $4\hslash k$ and $-4\hslash k$ momentum states with an efficiency of over 99% per Bloch cycle. In a vertical lattice, gravity-induced Bloch oscillations were demonstrated, from which the local gravitational acceleration was derived with a statistical uncertainty of $4\times {10}^{-5}$. A clear advantage of ${\text{He}}^{*}$ over other atoms is that it can be detected with a microchannel plate detector with near unity efficiency, and this enabled observation of Bloch oscillations up to 12 s even though the number of atoms decreased by three orders of magnitude. These results establish ${\text{He}}^{*}$ as a promising candidate for future precision measurements with atom interferometry.

In a standard interferometry experiment, one measures the phase difference between two paths by recombining the two wave packets on a beam splitter. However, it has been recognized that the phase can also be estimated via local measurements by using an ancillary particle in a known superposition state. In this work, we review and further explicate these protocols for different types of particles (bosons or fermions, charged or uncharged), with a particular emphasis on the subtleties that arise when the phase is due to the coupling to an Abelian gauge field. In that case, we show that the measurable quantities are space-time loop integrals of the four-vector potential, enclosed by two identical particles or by a particle-antiparticle pair. Furthermore, we generalize our considerations to scenarios involving an arbitrary number of parties performing local measurements on a general charged fermionic state. Finally, as a concrete application, we analyze a recent proposal involving the time-dependent Aharonov-Bohm effect [C. Marletto and V. Vedral, Phys. Rev. Lett. 125, 040401 (2020)].

Reversing the effects of a quantum evolution, for example, as is done in error correction, is an important task for controlling quantum systems in order to produce reliable quantum devices. When the evolution is governed by a completely positive map, there exist reversibility conditions, known as the quantum error correcting code conditions, which are necessary and sufficient conditions for the reversibility of a quantum operation on a subspace, the code space. However, if we suppose that the evolution is not described by a completely positive map, necessary and sufficient conditions are not known. Here we consider evolutions that do not necessarily correspond to a completely positive map. We prove that the completely positive map error correcting code conditions can lead to a code space that is not in the domain of the map, meaning that the output of the map is not positive. A corollary to our theorem provides a class of relevant examples. Finally, we provide a set of sufficient conditions that will enable the use of quantum error correcting code conditions while ensuring positivity.

We study the dynamics of entanglement in a one-dimensional coupled-cavity array, with each cavity containing a two-level atom, via the Jaynes-Cummings-Hubbard (JCH) Hamiltonian in the single-excitation sector. The model features a rich variety of dynamical regimes that can be harnessed for entanglement control. The protocol is based on setting an excited atom above the ground state and further letting it evolve following the natural dynamics of the Hamiltonian. Here we focus on the concurrence between pairs of atoms and its relation to atom-field correlations and the involved free-field modes. We show that the extension and distribution pattern of pairwise entanglement can be manipulated through a judicious tuning of the atom-cavity coupling strength. By also including static noise in the cavity frequencies, we explore the onset of Anderson localization and its interplay with the atomic trapping known to take place in the strong-hopping regime. Remarkably, we find that the stronger the disorder is, the higher are the atom-field correlations, whereas the atomic concurrence responds nonmonotonically. Overall, our work offers a comprehensive account of the machinery of the single-excitation JCH Hamiltonian and contributes to the design of hybrid light-matter quantum networks.

We present a general approach to measurement-based quantum feedback that employs proportional and quantum state–(PaQS-) based feedback components to obtain locally optimal protocols. To demonstrate the power of the method, we first show that it reproduces many known feedback protocols and then apply it to generation of multipartite entanglement with an emphasis on remote entanglement, which requires spatially local feedback Hamiltonians. The symmetry of both measurement and feedback operators is found to be essential for construction of effective protocols. We show that under perfect measurement efficiency, entangled states can be reached with fidelity approaching unity under non-Markovian feedback control protocols, while Markovian protocols resulting from optimizing the feedback unitaries on ensemble-averaged states still yield fidelities above 94%. Application of the PaQS approach to generation of $N$-qubit $W$, general Dicke, and Greenberger-Horne-Zeilinger states shows that such entangled states can be efficiently generated with high fidelity, for up to $N=100$ in some cases.

Molecular quantum simulations with the variational quantum eigensolver (VQE) rely on ansatz states that approximate the molecular ground states. These ansatz states are generally defined by parametrized fermionic excitation operators and an initial reference state. Efficient ways to perform fermionic excitations are vital for the realization of the VQE on noisy intermediate-scale quantum computers. Here, we address this issue by first demonstrating circuits that perform qubit excitations, excitations that do not account for fermionic anticommutation relations. We then extend the functionality of these circuits to perform fermionic excitations. Compared to circuits constructed with the standard use of “$CNOT$ staircases”, our circuits offer a linear reduction in the number of $CNOT$ gates, by a factor of 2 (8) per single (double) qubit or fermionic excitation, respectively. Our results reduce the requirements for near-term realizations of quantum molecular simulations.

We study the resonant two-photon ionization of neutral atoms by a combination of twisted and plane-wave light within a fully relativistic framework. In particular, the ionization of an isotropic ensemble of neutral sodium atoms ($Z=11$) from their ground $3{}^2{S}_{1/2}$ state via the $3{}^2{P}_{3/2}$ level is considered. We investigate in details the influence of the kinematic parameters of incoming twisted radiation on the photoelectron angular distribution and the circular dichroism. Moreover, we study the influence of the geometry of the process on these quantities. This is done by changing the propagation directions of the incoming twisted and plane-wave light. It is found that the dependence on the kinematic parameters of the twisted photon is the strongest if the plane-wave and twisted light beams are perpendicular to each other.