Quantum Principles of Two-Level Atomic Spectroscopy

Is an atom more likely to scatter a photon with an exponentially rising or decaying temporal profile? We try to answer this question experimentally and investigate the scattering of heralded photons from a single atom in free-space [1]. We use a single Rubidium atom trapped in optical tweezers and prepared in the groundstate of a cyclic dipole transition as a textbook-like two-level system. A time-ordered photon pair source, in conjunction with an asymmetric cavity, generates heralded single photons with an exponentially decaying or rising temporal profile [2, 3]. The heralded photons are resonant with the atomic transition and have a bandwidth comparable to the atomic linewidth. The photons are strongly focused onto the atom by a large numerical aperture lens. We study the scattering dynamics by measuring the atomic emission and the reduction in the number of transmitted photons. We perform the scattering experiment for photons with exponentially decaying and rising temporal envelopes and find that the atomic dynamics depend on the temporal profile of the photon. The atomic absorption is shorter but has a higher maximum for the rising photon than for the the decaying one. Interestingly, the overall probability that the photon is scattered by the atom is similar for decaying and rising photons.

We investigate a hybrid electro-mechanical system consisting of a pair of charged macroscopic mechanical oscillators coupled to a small ensemble of Rydberg atoms. The resonant dipole-dipole coupling between an internal atomic Rydberg transition and the mechanics allows cooling to its motional ground state with a single atom despite the considerable mass imbalance between the two subsystems. We show that the rich electronic spectrum of Rydberg atoms, combined with their high degree of optical control, paves the way towards implementing various quantum-control protocol for the mechanical oscillators.

The generation, distribution and control of entanglement across quantum networks is one of the main goals of quantum information science. In previous studies, hyperfine ground states of single atoms or atomic ensembles have been entangled with spontaneously emitted light. The probabilistic character of the spontaneous emission process leads to long entanglement generation times, limiting realized network implementations to just two nodes. The success probability for atom-photon entanglement protocols can be increased by confining a single atom in a high-finesse optical cavity. Alternatively, quantum networks with superior scaling properties could be achieved using entanglement between light fields and atoms in quantum superpositions of the ground and highly excited (Rydberg) electronic states. Here we report the generation of such entanglement. The dephasing of the optical atomic coherence is inhibited by state-insensitive confinement of both the ground and Rydberg states of an ultracold atomic gas in an optical lattice. Our results pave the way for functional, many-node quantum networks capable of deterministic quantum logic operations between long-lived atomic memories.

Preparation of W state among spatially separated atomic ensembles collectively controlled by a single atom via adiabatic passage

Single-atom catalyst (SAC) has an electronic structure that is very different from its bulk counterparts, and has shown unexpectedly high specific activity with a significant reduction of noble metal usages although physical origins of such performance enhancements are still poorly understood. Herein, by means of density functional theory calculations, we for the first time investigate the great potential of single atom catalyst for CO2 electroreduction applications. In particular, we study a single transition metal atom anchored on the defective graphene with single or double vacancies, denoted as M@sv-Gr or M@dv-Gr, where M are various transition metals, as a CO2 reduction catalyst. Many SACs are indeed shown to be highly selective for CO2 reduction reaction over a competitive H2 evolution reaction due to a favorable adsorption of carboxyl or formate over hydrogen on the catalysts. On the basis of free energies, we found that the Pt@dv-Gr catalyst shows a remarkable reduction in the limiting potential for CH3OH production compared to any existing catalysts, synthesized or predicted (Figure 1). We focus on the Pt@dv-Gr to investigate the origin of improvement on the SACs compared to the transition metal. As shown in Figure 1, with the Pt@dv-Gr catalyst, all the intermediates are destabilized compared to those on Pt (211), but most importantly, the destabilization of *CO (0.98 eV) is much more noticeable than that of *CHO (0.42 eV), leading to a 0.49 V reduction in the limiting potential. We also observe that with SACs, the conventional scaling relation between the *CO binding and *CHO binding established for the bulk transition metal significantly deviates from linearity (Figure 2). We discuss features of SACs which contribute to the breakdown of scaling relation between *CO and *CHO, namely, the lack of atomic ensemble for adsorbates binding and the metal-support interactions that lead to the electronic structures conducive to the catalysis. Atomic Ensemble: The optimized geometries of the bare catalysts are shown for Pt@dv-Gr and Pt (211) in Figure 3. One can see that, for Pt (211), two surface Pt atoms are involved in the *CO bonding while only one Pt atom is bonding with *CHO, leading to a large destabilization in the relative free energies when going from *CO to *CHO. On the other hand, for Pt@dv-Gr, only one Pt atom is utilized for both *CO and *CHO binding, resulting in a much more moderate destabilization in relative free energies compared to Pt (211). Thus, the lack of Pt ensemble in the Pt@dv-Gr is responsible for a significantly weaker binding of *CO on the Pt@dv-Gr compared to the Pt (211) surface. Electronic Structure: The strong metal-support interaction affects the electronic structure of a metal atom in the SACs greatly. In Figure 4A, the Pt 5d density of states (DOS) in Pt@dv-Gr shows a significant orbital overlap with the C 2p orbitals of the graphene. The electron density isosurfaces (Figure 4B) illustrate that electron clouds of four carbon atoms surrounding the Pt atom are significantly hybridized with the Pt atom. The differential charge density map (Figure 4C) between the defective graphene and Pt@dv-Gr also suggests that the Pt atom is positively charged by electron transfer from the Pt atom to the defective graphene support. In this paper, we investigated the single atom catalysts (SACs) as a promising CO2 electroreduction catalyst using DFT calculations. The main findings of this work are as follows. (i) By comparing the free energies of the initial protonation steps for the CRR and HER, we found that all SACs can selectively reduce CO2 rather than producing H2. In particular, the predicted limiting potential for Pt@dv-Gr (-0.27 V) for CH3OH production is considerably less negative than the conventional transition metal catalysts. (ii) To understand the origin of the improvements in SACs, we investigated two aspects of the Pt@dv-Gr that affect the relative stability of *CO vs. *CHO. A one-fold bonding of *CO on Pt@dv-Gr due to a lack of atomic ensemble, as compared to the two-fold *CO bonding on the Pt (211) is responsible for the significant weakening of *CO binding on the Pt@dv-Gr. (iii) We investigated the electronic structure of Pt atom in the SAC to find the origin of the deviation of SACs from the conventional scaling relation of transition metals, which arises from the d-band center theory. We suggest that the strong electronic interaction between the d-orbital of metal atom and the p-orbital of graphene is responsible for the different behavior from the transition metal surfaces, as evidenced by the electron transfer and the overlap in the DOS. Figure 1

An exact analytical approach to study the time evolution of the interaction between a system of N two-level atoms with a single-mode cavity field is proposed. Supposing that at the initial moment the system of radiators is prepared in a superposition of states, the wave functions of the atom–field interaction for three and four atoms are presented exactly. In the case of an odd number of atoms in the cavity, the quantum Rabi frequencies have non-zero values; otherwise one zero value of the quantum Rabi frequency is characteristic of the even number of atoms. It was shown that with an increase of the odd number of atoms the non-zero quantum Rabi frequencies in the system increase too. It was established that a single atom has one quantum Rabi frequency, three atoms have two frequencies and five atoms have three. For the even number of atoms, a zero value of eigenstates of radiators in the interaction with a single cavity mode is observed. In this case the number of collective levels in the system is odd and the trapping states of atoms in the cavity are possible. From analytical solutions it follows that it is possible to realize the micro-maser regimes for three atoms choosing the flying time for which the radiators pass totally in the ground state. The dependence of the flying time on the number of atoms is established as well as the cavity state for which the atomic ensemble comes back to its initial state. The behavior of quantum fluctuations of photon numbers and atomic inversion during collective absorption and radiation is exactly analytically and numerically studied. The exact quantum solutions for these qubits, formed from two-level atoms, can be used in quantum processing of information encapsuled in the initial states of the atomic ensemble and the cavity field.

We analyze the operation of a novel sensor based on atom interferometry, which can achieve supra-classical sensitivity by exploiting quantum correlations in mixed states of many qubits. The interferometer is based on quantum gates which use coherently-controlled Rydberg interactions between a single atom (which acts as a control qubit) and an atomic ensemble (which provides register qubits). In principle, our scheme can achieve precision scaling with the size of the ensemble - which can extend to large numbers of atoms - while using only single-qubit operations on the control and bulk operations on the ensemble. We investigate realistic implementation of the interferometer, and our main aim is to develop a new approach to quantum metrology that can achieve quantum-enhanced measurement precision by exploiting coherent operations on large impure quantum states. We propose an experiment to demonstrate the enhanced sensitivity of the protocol, and to investigate a transition from classical to supra-classical sensitivity which occurs when using highly-mixed probe states.

The emission spectrum of a single atom inside an optomechanical cavity is studied in this paper. Our model consists of a single two-level atom coupled to a cavity with a moving end mirror. We numerically calculate the emission spectrum of the atom, taking the effect of the moving mirror into account. The dependence of the spectrum peak on the coupling between the moving mirror and the cavity field is analyzed. For weak cavity-mirror couplings, we expand the spectrum up to the first order of the coupling constant.

Recent years have seen tremendous progress in creating complex atomic many-body quantum systems. One approach is to use macroscopic, effectively thermodynamic ensembles of ultracold atoms to create quantum gases and strongly correlated states of matter, and to analyse the bulk properties of the ensemble. For example, bosonic and fermionic atoms in a Hubbard-regime optical lattice can be used for quantum simulations of solid-state models. The opposite approach is to build up microscopic quantum systems atom-by-atom, with complete control over all degrees of freedom. The atoms or ions act as qubits and allow the realization of quantum gates, with the goal of creating highly controllable quantum information systems. Until now, the macroscopic and microscopic strategies have been fairly disconnected. Here we present a quantum gas 'microscope' that bridges the two approaches, realizing a system in which atoms of a macroscopic ensemble are detected individually and a complete set of degrees of freedom for each of them is determined through preparation and measurement. By implementing a high-resolution optical imaging system, single atoms are detected with near-unity fidelity on individual sites of a Hubbard-regime optical lattice. The lattice itself is generated by projecting a holographic mask through the imaging system. It has an arbitrary geometry, chosen to support both strong tunnel coupling between lattice sites and strong on-site confinement. Our approach can be used to directly detect strongly correlated states of matter; in the context of condensed matter simulation, this corresponds to the detection of individual electrons in the simulated crystal. Also, the quantum gas microscope may enable addressing and read-out of large-scale quantum information systems based on ultracold atoms.

Tomography vs quantum control for a three-level atom

We propose a nonadiabatic non-Abelian geometric quantum operation scheme to realize universal quantum computation with mesoscopic Rydberg atoms. A single control atom entangles a mesoscopic ensemble of target atoms through long-range interactions between Rydberg states. We demonstrate theoretically that both the single qubit and two-qubit quantum gates can achieve high fidelities around or above 99.9% in ideal situations. Besides, to address the experimental issue of Rabi frequency fluctuation (Rabi error) in Rydberg atom and ensemble, we apply the dynamical-invariant-based zero systematic-error sensitivity (ZSS) optimal control theory to the proposed scheme. Our numerical simulations show that the average fidelity could be 99.98% for single ensemble qubit gate and 99.94% for two-qubit gate even when the Rabi frequency of the gate laser acquires 10% fluctuations. We also find that the optimized scheme can also reduce errors caused by higher-order perturbation terms in deriving the Hamiltonian of the ensemble atoms. To address the experimental issue of decoherence error between the ground state and Rydberg levels in Rydberg ensemble, we introduce a dispersive coupling regime between Rydberg and ground levels, based on which the Rydberg state is adiabatically discarded. The numerical simulation demonstrate that the quantum gate is enhanced. By combining strong Rydberg atom interactions, nonadiabatic geometric quantum computation, dynamical invariant and optimal control theory together, our scheme shows a new route to construct fast and robust quantum gates with mesoscopic atomic ensembles. Our study contributes to the ongoing effort in developing quantum information processing with Rydberg atoms trapped in optical lattices or tweezer arrays.

Abstract

A canonical transformation is performed on the conventional Hamiltonian for the electromagnetic radiation field and an assemblage of neutral molecules in interaction. The new Hamiltonian has interaction energies expressed in terms of the electromagnetic fields alone and these energies have direct physical significance. The terms linear in e are the multipole interactions, both electric and magnetic, and the term quadratic in e is a generalization of the elementary diamagnetic energy shift. The intermolecular Coulomb energies have cancelled with transverse polarization fields in the new Hamiltonian, although the intramolecular Coulomb potentials are left unaffected. The equations of motion that follow from the new Hamiltonian are deduced. They are the so-called atomic-field equations for the Maxwell fields and Schrödinger equation for an electron wave in a transverse electromagnetic field. The former are the microscopic analogues of Maxwell’s equations in a medium (not restricted to dipole polarization fields) and the latter are dependent on the field strengths alone (not explicit functions of the vector potential).

In this second paper, we complete the classical description of an isolated system of “charged positive-energy particles, with Grassmann-valued electric charges and mutual Coulomb interaction, plus a transverse electromagnetic field” in the rest-frame instant form of dynamics. In particular, we show how to determine a collective variable associated with the internal 3-center of mass on the instantaneous 3-spaces, to be eliminated with the constraints [Formula: see text]. Here, [Formula: see text] is the Lorentz boost generator in the unfaithful internal realization of the Poincaré group and its vanishing is the gauge-fixing to the rest-frame conditions [Formula: see text]. We show how to find this collective variable for the following isolated systems: (a) charged particles with a Coulomb plus Darwin mutual interaction; (b) transverse radiation field; (c) charged particles with a mutual Coulomb interaction plus a transverse electro-magnetic field. Then we define the Dixon multipolar expansion for the open particle subsystem. We also define the relativistic electric dipole approximation of atomic physics in the rest-frame instant form and we find a possible relativistic generalization of the electric dipole representation.

A single trapped neutral atom is used for precise subwavelength intensity measurements. Quantum jumps from a dark to a bright atomic state are used to boost signal-to-noise and avoid systematic errors.