Superposition Of Atomic States Research Articles

Transport of ultracold atoms in superpositions of S - and D -band states in a moving optical lattice

Ultracold atoms in a moving optical lattice with high controllability are a feasible platform to research the transport phenomenon. Here, we study the transport process of ultracold atoms at the $D$ band in a one-dimensional optical lattice and manipulate the transport of superposition states with different superposition weights of $S$-band and $D$-band atoms. In the experiment, we first load ultracold atoms into an optical lattice using the shortcut method and then accelerate the optical lattice by scanning the phase of lattice beams. The atomic transport at the $D$ band and $S$ band is demonstrated, respectively. The group velocity of atoms at the $D$ band is opposite to that at the $S$ band. By preparing superposition states with different superposition weights of the $D$-band and $S$-band atoms, we realize the manipulation of atomic group velocity from positive to negative, and observe the quantum interference between atoms at different bands. The influence of the lattice depth and acceleration on the transport process is also studied. Moreover, the multiorbital simulations are coincident with the experimental results. Our paper sheds light on the transport process of ultracold atoms at higher bands in optical lattices and provides a useful method to manipulate the transport of atomic superposition states.

Electrometry of a single resonator mode at a Rydberg-atom–superconducting-circuit interface

The electric-field distribution in a single mode of a $\ensuremath{\lambda}/4$ superconducting coplanar waveguide (CPW) microwave resonator has been probed using beams of helium Rydberg atoms. In the experiments the atoms were prepared in the $1\mathrm{s}55\mathrm{s}{\phantom{\rule{0.16em}{0ex}}}^{3}{\mathrm{S}}_{1}$ Rydberg level by laser photoexcitation. They then traveled over the CPW resonator that was fabricated on a NbN superconducting chip operated at 3.8 K. The resonator was driven at its third-harmonic frequency, near resonant with the two-photon $1\mathrm{s}55\mathrm{s}{\phantom{\rule{0.16em}{0ex}}}^{3}{\mathrm{S}}_{1}\ensuremath{\rightarrow}1\mathrm{s}56\mathrm{s}{\phantom{\rule{0.16em}{0ex}}}^{3}{\mathrm{S}}_{1}$ transition at ${\ensuremath{\omega}}_{55\mathrm{s},\phantom{\rule{0.16em}{0ex}}56\mathrm{s}}/2=2\ensuremath{\pi}\phantom{\rule{0.16em}{0ex}}\ifmmode\times\else\texttimes\fi{}\phantom{\rule{0.16em}{0ex}}19.556\phantom{\rule{0.16em}{0ex}}499$ GHz. The coherence times of the atom--resonator-field interaction were determined at selected locations above the resonator by time-domain measurements of Rabi oscillations and found to be up to $0.8\phantom{\rule{0.16em}{0ex}}\ensuremath{\mu}\mathrm{s}$ for Rabi frequencies of $\ensuremath{\sim}2\ensuremath{\pi}\phantom{\rule{0.16em}{0ex}}\ifmmode\times\else\texttimes\fi{}\phantom{\rule{0.16em}{0ex}}3$ MHz. The coherence times of the atomic superposition states, generated following the interaction of the atoms with the microwave field in the resonator, were inferred from high-resolution cavity-enhanced Ramsey spectra to be $\ensuremath{\sim}2.5\phantom{\rule{0.16em}{0ex}}\ensuremath{\mu}\mathrm{s}$. These Ramsey spectra also allowed the measurement of residual uncanceled dc electric fields of $26.6\ifmmode\pm\else\textpm\fi{}0.6$ mV/cm at the position of the atoms $\ensuremath{\sim}300\phantom{\rule{0.16em}{0ex}}\ensuremath{\mu}\mathrm{m}$ above the surface of the superconducting chip. These results represent an essential step toward applications of hybrid systems, comprising Rydberg atoms coherently coupled to superconducting microwave circuits, in quantum optics and quantum information processing.

Non-equilibrium quantum dynamics and formation of the Bose polaron

Advancing our understanding of non-equilibrium phenomena in quantum many-body systems remains one of the greatest challenges in physics. Here we report on the experimental observation of a paradigmatic many-body problem, namely the non-equilibrium dynamics of a quantum impurity immersed in a bosonic environment1,2. We use an interferometric technique to prepare coherent superposition states of atoms in a Bose–Einstein condensate with a small impurity-state component, and monitor the evolution of such quantum superpositions into polaronic quasiparticles. These results offer a systematic picture of polaron formation3–7 from weak to strong impurity interactions. They reveal three distinct regimes of evolution with dynamical transitions that provide a link between few-body processes and many-body dynamics. Our measurements reveal universal dynamical behaviour in interacting many-body systems and demonstrate new pathways to study non-equilibrium quantum phenomena. Quantum impurities immersed in a bosonic environment can evolve into polaronic quasiparticles, so-called polarons. Interferometric measurement reveals this transition, which involves three different regimes dominated by few-body and many-body dynamics.

Asymmetries in ionization of atomic superposition states by ultrashort laser pulses

Progress in ultrafast science allows for probing quantum superposition states with ultrashort laser pulses in the new regime where several linear and nonlinear ionization pathways compete. Interferences of pathways can be observed in the photoelectron angular distribution and in the past they have been analyzed for atoms and molecules in a single quantum state via anisotropy and asymmetry parameters. Those conventional parameters, however, do not provide comprehensive tools for probing superposition states in the emerging research area of bright and ultrashort light sources, such as free-electron lasers and high-order harmonic generation. We propose a new set of generalized asymmetry parameters which are sensitive to interference effects in the photoionization and the interplay of competing pathways as the laser pulse duration is shortened and the laser intensity is increased. The relevance of the parameters is demonstrated using results of state-of-the-art numerical solutions of the time-dependent Schrödinger equation for ionization of helium atom and neon atom.

Strict experimental test of macroscopic realism in a light-matter-interfaced system

Macroscopic realism is a classical worldview that a macroscopic system is always determinately in one of the two or more macroscopically distinguishable states available to it, and so is never in a superposition of these states. The question of whether there is a fundamental limitation on the possibility to observe quantum phenomena at the macroscopic scale remains unclear. Here we implement a strict and simple protocol to test macroscopic realism in a light-matter interfaced system. We create a micro-macro entanglement with two macroscopically distinguishable solid-state components and rule out those theories which would deny coherent superpositions of up to 76 atomic excitations shared by 10^10 ions in two separated solids. These results provide a general method to enhance the size of superposition states of atoms by utilizing quantum memory techniques and to push the envelope of macroscopicity at higher levels.

Entropy squeezing for three-level atom interacting with a single-mode field**Project supported by the National Natural Science Foundation of China (Grant No. 11374096).

The entropy squeezing for a three-level atom interacting with a single-model field is studied. A general definition of entropy squeezing for three-level atom is given according to entropic uncertainty relation of three-level system, and the calculation formalism of entropy is derived for a cascade three-level atom. By using numerical calculation, the entropy squeezing properties of a cascade three-level atom are examined. Our results show that, three-level atom can generate obvious entropy squeezing effect via choosing appropriate superposition state of three-level atom. Our results are meaningful for preparing three-level system information resources with ultra-low quantum noise.

Near-circularly polarized isolated attosecond pulse generation from coherent superposition state by a circularly polarized laser field

We theoretically investigate high-order harmonic generation (HHG) from a coherent superposition state of hydrogen atom in a circularly polarized (CP) laser field. The results show that, driven by the CP field, HHG from the coherent superposition state is enhanced by 4 to 5 orders of magnitude compared to that from the ground state. The enhanced intensity is comparable to that of the ground state in a linearly polarized laser field. Based on the classical and quantum analyses, we demonstrate that HHG in the CP laser field mainly arises from the recombination of electrons ionized at non-zero initial positions. The enhancement of HHG from the coherent superposition state is due to the higher ionization rate and also the larger probability density of electrons located far from the nucleus of the involved excited state. The obtained harmonic spectra support the generation of intense isolated attosecond pulses (IAPs) with the ellipticity as high as 0.93. Moreover, we show that the generation of IAPs with large ellipticity is robust against the variation of the carrier envelope phase (CEP) of the laser field. Our results provide a new route toward generating near-CP IAPs, which will be beneficial for ultrafast detection of chiral-sensitive light-matter interactions.

Observation of dressed states of distant atoms with delocalized photons in coupled-cavities quantum electrodynamics

In a cavity quantum electrodynamics (QED) system, where atoms coherently interact with photons in a cavity, the eigenstates of the system are the superposition states of atoms and cavity photons, the so-called dressed states of atoms. When two cavities are connected by an optical fiber with negligible loss, the coherent coupling between the cavities gives rise to photonic normal modes. One of these normal modes is the fiber-dark mode, in which photons are delocalized in the two distant cavities. Here we demonstrate the setting of coupled-cavities QED, where two nanofiber cavity-QED systems are coherently connected by a meter-long low-loss channel in an all-fiber fashion. Specifically, we observe dressed states of distant atoms with delocalized photons of the fiber-dark normal mode. Our system will provide a platform for the study of delocalized atomic and photonic states, photonic many-body physics, and distributed quantum computation.

Lattice-induced photon scattering in an optical lattice clock

We investigate scattering of lattice laser radiation in a strontium optical lattice clock and its implications for operating clocks at interrogation times up to several tens of seconds. Rayleigh scattering does not cause significant decoherence of the atomic superposition state near a magic wavelength. Among the Raman scattering processes, lattice-induced decay of the excited state $(5s5p)\,{}^{3}\mathrm{P}_{0}$ to the ground state $(5s^2)\,{}^{1}\mathrm{S}_{0}$ via the state $(5s5p)\,{}^{3}\mathrm{P}_{1}$ is particularly relevant, as it reduces the effective lifetime of the excited state and gives rise to quantum projection noise in spectroscopy. We observe this process in our experiment and find a decay rate of $556(15)\times 10^{-6}\,\mathrm{s}^{-1}$ per photon recoil energy $E_\mathrm{r}$ of effective lattice depth, which agrees well with the rate we predict from atomic data. We also derive a natural lifetime $\tau = 330(140)\,\mathrm{s}$ of the excited state ${}^{3}\mathrm{P}_{0}$ from our observations. Lattice-induced decay thus exceeds spontaneous decay at typical lattice depths used by present clocks. It eventually limits interrogation times in clocks restricted to high-intensity lattices, but can be largely avoided, e.g., by operating them with shallow lattice potentials.

Atomic-state diagnostics and optimization in cold-atom experiments

We report on the creation, observation and optimization of superposition states of cold atoms. In our experiments, rubidium atoms are prepared in a magneto-optical trap and later, after switching off the trapping fields, Faraday rotation of a weak probe beam is used to characterize atomic states prepared by application of appropriate light pulses and external magnetic fields. We discuss the signatures of polarization and alignment of atomic spin states and identify main factors responsible for deterioration of the atomic number and their coherence and present means for their optimization, like relaxation in the dark with the strobed probing. These results may be used for controlled preparation of cold atom samples and in situ magnetometry of static and transient fields.

Coupling ultracold atoms to a superconducting coplanar waveguide resonator

Ensembles of trapped atoms interacting with on-chip microwave resonators are considered as promising systems for the realization of quantum memories, novel quantum gates, and interfaces between the microwave and optical regime. Here, we demonstrate coupling of magnetically trapped ultracold Rb ground-state atoms to a coherently driven superconducting coplanar resonator on an integrated atom chip. When the cavity is driven off-resonance from the atomic transition, the microwave field strength in the cavity can be measured through observation of the AC shift of the atomic hyperfine transition frequency. When driving the cavity in resonance with the atoms, we observe Rabi oscillations between hyperfine states, demonstrating coherent control of the atomic states through the cavity field. These observations enable the preparation of coherent atomic superposition states, which are required for the implementation of an atomic quantum memory.

Generation and Preparation of the Sustained Optimal Entropy Squeezing State of a Motional Atom Inside Vacuum Cavity

Considering two two-level atoms initially in Bell state, we send one atom into a vacuum cavity while leaving the other outside, and consider the motion of atom inside the cavity. Using quantum information entropy squeezing theory, the time evolution of the entropy squeezing factor of atom inside the cavity is discussed for two cases, i.e., before and after performing rotation operations and measuring atom outside, the influences of the field mode structure and atomic motions on the atomic entropy squeezing are evaluated. It is shown that atom inside the cavity has no entropy squeezing phenomenon before operating atom outside the cavity. However, the optimal entropy squeezing phenomenon of period T = 2π/p emerges and constant entropy squeezing phenomenon can occur by adjusting rotation operation to R(π/4), and setting the field mode structure parameter 0 50, a sustained optimal entropy squeezing state (SOESS) can be generated. We also present the schematic circuit diagram of preparation of SOESS. Our proposal provides a possible way for the initial decoherent state recovering into sustained maximal coherent superposition state of single atom in the quantum noise environment.

Atom–light superposition oscillation and Ramsey-like atom–light interferometer

Coherent wave splitting is crucial in interferometers. Normally, the waves after this splitting are of the same type. But recent progress in interaction between atom and light has led to the coherent conversion of photon to atomic excitation. This makes it possible to split an incoming light wave into a coherent superposition state of atom and light and paves the way for an interferometer made of different types of waves. Here we report on a Rabi-like coherent-superposition oscillation observed between atom and light and a coherent mixing of light wave with excited atomic spin wave in a Raman process. We construct a new kind of hybrid interferometer based on the atom-light coherent superposition state. Interference fringes are observed in both optical output intensity and atomic output in terms of the atomic spin wave strength when we scan either or both of the optical and atomic phases. Such a hybrid interferometer can be used to interrogate atomic states by optical detection and will find its applications in precision measurement and quantum control of atoms and light.

Phase Locking a Clock Oscillator to a Coherent Atomic Ensemble

The sensitivity of an atomic interferometer increases when the phase evolution of its quantum superposition state is measured over a longer interrogation interval. In practice, a limit is set by the measurement process, which returns not the phase, but its projection in terms of population difference on two energetic levels. The phase interval over which the relation can be inverted is thus limited to the interval $[-\pi/2,\pi/2]$; going beyond it introduces an ambiguity in the read out, hence a sensitivity loss. Here, we extend the unambiguous interval to probe the phase evolution of an atomic ensemble using coherence preserving measurements and phase corrections, and demonstrate the phase lock of the clock oscillator to an atomic superposition state. We propose a protocol based on the phase lock to improve atomic clocks under local oscillator noise, and foresee the application to other atomic interferometers such as inertial sensors.

Macroscopic optomechanical superposition via periodic qubit flipping

We propose a scheme to generate macroscopic superpositions of well-distinguishable coherent states in an optomechanical system via periodic qubit flipping. Our scheme does not require the single-photon strong-coupling rate of an optomechanical system. The generated mechanical superposition state can be reconstructed using mechanical quantum-state reconstruction. The proposed scheme relies on recycling of an atom, fast atomic qubit flipping, and coherent state mapping between a single-photon superposition state and an atomic superposition state. We discuss the experimental feasibility of our proposal under current technology.

Creation of Coherent Superposition State by Stimulated Raman Adiabatic Passage in Serial Multi-Λ-Type System

We propose a scheme for creating coherent atomic superposition states via the technique of stimulated Raman adiabatic passage (STIRAP) in a Λ-type system where final states are composed of manifold of levels and the intermediate levels could be more than one level. If the pump pulses and Stokes pulses are kept in the same order of ordinary STIRAP, through the control the delay time between the Stokes pulses and pump pulse, we could create arbitrary superposition states in the manifold of levels.

A strong single attosecond pulse generation from an atomic superposition state with chirped laser fields

We numerically investigate the chirp-depending of supercontinuum generation with preparing He+ ions in a coherent superposition of the states 1s and 2s. The results show that the initial population of the 2s state can lead to the formation of intense supercontinuum in spectrum. By precise control of chirp parameter, the spectral width and intensity of supercontinuum harmonics increase. Moreover, with a synchronous decrease of pulse durations, the bandwidth of the intense supercontinuum increases. The time–frequency characteristic of harmonics reveals that the long quantum-path is dominated in supercontinuum-region. As a result, an intense 7-as isolated pulse with a bandwidth of 570eV can be achieved.

Manipulation and coherence of ultra-cold atoms on a superconducting atom chip

The coherence of quantum systems is crucial to quantum information processing. Although superconducting qubits can process quantum information at microelectronics rates, it remains a challenge to preserve the coherence and therefore the quantum character of the information in these systems. An alternative is to share the tasks between different quantum platforms, for example, cold atoms storing the quantum information processed by superconducting circuits. Here we characterize the coherence of superposition states of (87)Rb atoms magnetically trapped on a superconducting atom chip. We load atoms into a persistent-current trap engineered next to a coplanar microwave resonator structure, and observe that the coherence of hyperfine ground states is preserved for several seconds. We show that large ensembles of a million of thermal atoms below 350 nK temperature and pure Bose-Einstein condensates with 3.5 × 10(5) atoms can be prepared and manipulated at the superconducting interface. This opens the path towards the rich dynamics of strong collective coupling regimes.

The influence of the relative phase on the interaction between a single mode cavity field and a four-level N-type atom

We study the interaction of a four-level N - type atom with a single mode cavity field when the initial phases of the cavity field and atomic superposition state are considered. We solve the model when the field and atom are initially prepared in a coherent state and coherent superposition of its excited and ground states, respectively. The collapse-revival, the anti-bunching of photons, the normal squeezing and the coherent phenomena have been discussed. The effects of the relative phase and detuning parameter on these phenomena are examined. We noticed that the presence of the relative phase and detuning parameter have an important effect on the properties of these phenomena.

Optical echo holography

The basic physics and applications of an unconventional area in holography that is based on the interference of light-induced atomic coherent superposition states in a resonant medium are discussed.