It is shown that the electrostatic potential of atomic nucleus "seen" by a fast charged projectile at short distances is smeared quantum mechanically due to nucleus motion around the atomic center of inertia. For example, the "positive charge cloud" size in the Hydrogen ground state is much larger than the proper proton size. It is even bigger for the target atoms in excited initial states. The elastic scattering at large angles is generally weaker than the Rutherford one since the effective potential at short distances is softer than the Colombian one due to a natural "cutoff". In addition, the large angle scattering leads to the target atom excitations due to pushing the nucleus (=> inelastic processes). The Rutherford cross section is in fact the inclusive rather than the elastic one. These results are analogous to the QED ones. The difference and the value of presented below non relativistic atomic calculations is in non perturbatively (exact) nucleus "dressing" that immediately leads to correct physical results and to significant technical simplifications. In these respects the nucleus bound in an atom is a simple but a rather realistic model of a "dressed" charge in the QFT. This idea is briefly demonstrated on the real electron model (electronium) that is made free from infinities.
A method to interpret probe spectra of driven degenerate atomic systems is discussed. The dressed-atom multiphoton spectroscopy (DAMS) is based on a dressing of the atomic system with the strong coupling field, followed by a perturbative treatment of the probe field interaction. As example, we apply the DAMS to provide a clear interpretation for anomalous electromagnetically induced absorption (EIA), which cannot be explained by spontaneous transfer of coherence. We show that anomalous EIA arises from quantum interference between competing two-photon transitions, and explain the different depe…
We theoretically study trapped ions that are immersed in an ultracold gas of Rydberg-dressed atoms. By off-resonant coupling on a dipole-forbidden transition, the adiabatic atom-ion potential can be made repulsive. We study the energy exchange between the atoms and a single trapped ion and find that Langevin collisions are inhibited in the ultracold regime for these repulsive interactions. Therefore, the proposed system avoids recently observed ion heating in hybrid atom-ion systems caused by coupling to the ion's radio frequency trapping field and retains ultracold temperatures even in the pr…
We demonstrate the trapping of cold $^{87}Rb$ atoms in a toroidal geometry using a radio frequency (rf) dressed quadrupole magnetic trap formed by superposing a strong rf-field on a quadrupole trap. This rf-dressed quadrupole trap has the minimum potential away from the quadrupole trap centre on a circular path which facilitates trapping in toroidal geometry. In these experiments, the laser cooled atoms were first trapped in a quadrupole trap, then cooled evaporatively using a weak rf-field, and finally trapped in an rf-dressed quadrupole trap. The radius of the toroid could be varied by varyi…
In Rydberg dressed ultra-cold gases, ground state atoms inherit properties of a weakly admixed Rydberg state, such as sensitivity to long-range interactions. We show that through hyperfine-state dependent interactions, a pair of atom clouds can evolve into a spin and subsequently into a spatial Schrödinger's cat state: The pair, containing 20 atoms in total, is in a coherent superposition of two configurations, with cloud locations separated by micrometers. The mesoscopic nature of the superposition state can be proven with absorption imaging, while the coherence can be revealed though recombi…
Using a Direct Simulation Monte Carlo technique, we have studied the time evolution of a cold atom cloud interacting with a time dependent radio frequency (rf) dressed state potential. Exposure of a cloud of $^{87}Rb$ atoms, trapped in a quadrupole magnetic trap, to a time dependent rf-field with increasing amplitude and decreasing frequency, shows a variation in the number of trapped atoms and the overall shape of the atom cloud. It is shown by simulations that, initially at lower rf-field strength, the rf-field results in ejection of atoms from the trap, leading to evaporative cooling of the…
We demonstrate finite range binding potentials between pairs of Rydberg atoms interacting with each other via attractive and repulsive van der Waals potentials and driven by a microwave field. We show that, using destructive quantum interference to cancel single-atom Rydberg excitation, the Rydberg-dimer states can be selectively and coherently populated from the two-atom ground state. This can be used to realize a two-qubit interaction gate which is not susceptible to mechanical forces between the atoms and is therefore immune to motional decoherence.
We examine interactions between atoms continuously and coherently driven between the ground state and a Rydberg state, producing "Rydberg-dressed atoms." Because of the large dipolar coupling between two Rydberg atoms, a small admixture of Rydberg character into a ground state can produce an atom with a dipole moment of a few Debye, the appropriate size to observe interesting dipolar physics effects in cold atom systems. We have calculated the interaction energies for atoms that interact via the dipole-dipole interaction and find that due to blockade effects, the R-dependent two-atom interacti…
Neutral atoms are building blocks of ground-up quantum many-body systems. Well-controlled and high-fidelity entangling gates are an essential component for realizing complex neutral atom architectures for quantum computing, quantum simulation, and measurement with precision better than the standard quantum limit. In this Letter we report the realization of a Mølmer-Sørensen unitary between two neutral atoms, based on adiabatic single-photon dressing to Rydberg levels. We show that this technique is highly robust to noise sources and experimental imperfections that have limited the fidelity of …
We study an architecture for implementing adiabatic quantum computation with trapped neutral atoms. Ground state atoms are dressed by laser fields in a manner conditional on the Rydberg blockade mechanism, thereby providing the requisite entangling interactions. As a benchmark we study the performance of a Quadratic Unconstrained Binary Optimization (QUBO) problem whose solution is found in the ground state spin configuration of an Ising-like model. We model a realistic architecture, including details of the atomic implementation, with qubits encoded into the clock states of 133Cs, effective B…
Controlling quantum entanglement between parts of a many-body system is the key to unlocking the power of quantum information processing for applications such as quantum computation, high-precision sensing, and simulation of many-body physics. Spin degrees of freedom of ultracold neutral atoms in their ground electronic state provide a natural platform given their long coherence times and our ability to control them with magneto-optical fields, but creating strong coherent coupling between spins has been challenging. We demonstrate a Rydberg-dressed ground-state blockade that provides a strong…
The addition of a weak oscillating field modifying strongly dressed spins enhances and enriches the system quantum dynamics. Through low-order harmonic mixing the bichromatic driving generates additional rectified static field acting on the spin system. The secondary field allows for a fine tuning of the atomic response and produces effects not accessible with a single dressing field, such as a spatial triaxial anisotropy of the spin coupling constants and acceleration of the spin dynamics. This tuning-dressed configuration introduces an extra handle for the system full engineering for quantum…
Non-adiabatic decay rates for a radio-frequency dressed magnetic trap are calculated using Fermi's Golden Rule: that is, we examine the probability for a single atom to make transitions out of the dressed trap and into a continuum in the adiabatic limit, where perturbation theory can be applied. This approach can be compared to the semi-classical Landau-Zener theory of a resonant dressed atom trap, and it is found that, when carefully implemented, the Landau-Zener theory overestimates the rate of non-adiabatic spin flip transitions in the adiabatic limit. This indicates that care is needed whe…
Optical lattice clock systems with ultra-cold strontium-88 atoms have been used to demonstrate superradiant lasing and magnetic field-controlled optical transmission. We explain these phenomena theoretically with a rigorous model for three-level atoms coupled to a single cavity mode. We identify a class of dark atom-light dressed states which become accessible due to mixing with bright dressed states in the presence of a magnetic field. We predict that these states, under moderate incoherent pumping, lead to lasing with a linewidth of only tens of Hz, orders of magnitude smaller than the cavit…
In dense atomic gases the interaction between transition dipoles and photons leads to the formation of many-body states with collective dissipation and long-ranged forces. Despite decades of research, a full understanding of this paradigmatic many-body problem is still lacking. Here, we put forward and explore a scenario in which a dense atomic gas is weakly excited by an off-resonant laser field. We develop the theory for describing such dressed many-body ensembles and show that collective excitations are responsible for the emergence of many-body interactions, i.e. effective potentials that …
Atom-atom interactions within a small volume were investigated through the excitation of ultracold Rb atoms. The application of microwaves enhances these interactions, causing the suppression of Rydberg state excitation. The suppression of Rydberg atom excitation was both qualitatively observed and quantitatively analyzed using a universal scaling law, giving a measure of the atom-atom interaction strength in agreement with theoretical prediction.
We develop the generalized rotating-wave approximation (GRWA) approach (Phys. Rev. Lett. 99, 173601 (2007)) to study the single-photon scattering on a two-level system (TLS) with arbitrarily strong coupling to a local mode in a one-dimensional (1D) coupled resonator array. We calculate the scattering amplitudes analytically, and the independent numerical results show that our approach works well in a broad parameter region. Especially, when the resonator mode is faroff resonance with the TLS, we obtain more reasonable results than the ones from the standard adiabatic approximation. Our approac…
We calculate the transient absorption of an isolated attosecond pulse by helium atoms subject to a delayed infrared (\ir) laser pulse. With the central frequency of the broad attosecond spectrum near the ionization threshold, the absorption spectrum is strongly modulated at the sub-\ir-cycle level. Given that the absorption spectrum results from a time-integrated measurement, we investigate the extent to which the delay-dependence of the absorption yields information about the attosecond dynamics of the atom-field energy exchange. We find two configurations in which this is possible. The first…
In this work, the RF-dressed potentials generated using a static magnetic field of a quadrupole trap and various radio frequency (RF) fields, have been theoretically investigated for trapping and manipulations of cold atoms in a two-dimensional (2D) geometry. It is shown that, in this scheme, the RF fields of some particular polarizations and phases can give rise to some novel static and time-dependent anisotropic two-dimensional potentials which are useful to trap and manipulate the cold atoms in the 2D geometry. The generated time-dependent 2D potentials, rotating on the circular ring, can b…
The giant electro-optical response of Rydberg atoms manifests itself in the emergence of sidebands in the Rydberg excitation spectrum if the atom is exposed to a radio-frequency (RF) electric field. Here we report on the study of RF-dressed Rydberg atoms inside hollow-core photonic crystal fibres (HC-PCF), a system that enables the use of low modulation voltages and offers the prospect of miniaturised vapour-based electro-optical devices. Narrow spectroscopic features caused by the RF field are observed for modulation frequencies up to 500 MHz.
We investigate the absorption line shapes of laser-dressed atoms beyond the single-atom response, by using extreme ultraviolet (XUV) attosecond pulse trains to probe an optically thick helium target under the influence of a strong infrared (IR) field. We study the interplay between the IR-induced phase shift of the microscopic time-dependent dipole moment and the resonant-propagation-induced reshaping of the macroscopic XUV pulse. Our experimental and theoretical results show that as the optical depth increases, this interplay leads initially to a broadening of the IR-modified line shape, and …
We evaluate the impact that nonlinear Zeeman shifts have on resonant radio-frequency (RF) dressed traps in an atom-chip configuration. The degeneracy of the resonance between Zeeman levels is lifted at large intensities of a static field, modifying the spatial dependence of the atomic adiabatic potential. In this context, we find effects that are important for the next generation of atom chips with tight trapping: in particular, that the vibrational frequency of the atom trap is sensitive to the RF frequency and, depending on the sign of the Landé factor, can produce significantly weaker, or t…
We consider a system consisting of an atom in the dipole approximation, coupled to the electromagnetic field. Using recently introduced renormalized coordinates and dressed states, we give a non-perturbative solution to the atom radiation process. From this formalism a non-exponential decay law naturally emerges. However, at least for low frequencies and weak coupling, there is only a very small, practically non-detectable, deviation from a purely exponential decay, in agreement with all previous results in the literature.
Trapping potentials and quantum gates for microwave-dressed Rydberg atoms on an atom chip
Freie Universität Berlin（柏林自由大学）；Center for Quantum Science and Technologies, FORTH（量子科学与技术中心，FORTH）；University of Crete（克里特大学）；German Research Center for Artificial Intelligence（德国人工智能研究中心）；Eberhard Karls Universität Tübingen（蒂宾根大学）
The derivation of approximate wave functions for an electron submitted to both a coulomb and a time-dependent laser electric fields, the so-called Coulomb-Volkov (CV) state, is addressed. Despite its derivation for continuum states does not exhibit any particular problem within the framework of the standard theory of quantum mechanics (QM), difficulties arise when considering an initially bound atomic state. Indeed the natural way of translating the unperturbed momentum by the laser vector potential is no longer possible since a bound state does not exhibit a plane wave form including explicit…
We have recorded fluorescence spectra of the atomic rubidium D-lines in the presence of several hundreds of bars buffer gas pressure. With additional saturation broadening a spectral linewidth comparable to the thermal energy of the atoms in the heated gas cell is achieved. An intensity-dependent blue asymmetry of the spectra is observed, which becomes increasingly pronounced when extrapolating to infinitely high light intensity. We interpret our results as evidence for the dressed (coupled atom-light) states to approach thermal equilibrium.
We show theoretically that by applying a bichromatic electromagnetic field, the dressed states of a monochromatically driven two-level atom can be pumped into a coherent superposition termed as dressed-state coherent population trapping. Such effect can be viewed as a new doorknob to manipulate a two-level system via its control over dressed-state populations. Application of this effect in the precision measurement of Rabi frequency, the unexpected population inversion and lasing without inversion are discussed to demonstrate such controllability.
We introduce a method to dispersively detect alkali atoms in radio-frequency dressed states. In particular, we use dressed detection to measure populations and population differences of atoms prepared in their clock states. Linear birefringence of the atomic medium enables atom number detection via polarisation homodyning, a form of common path interferometry. In order to achieve low technical noise levels, we perform optical sideband detection after adiabatic transformation of bare states into dressed states. The balanced homodyne signal then oscillates independently of field fluctuations at …
We theoretically examine the neutral atom-molecule analogue of the anomalous quantum correlations between degenerate electrons, i.e., Cooper pairs, that are responsible for superconductivity. Based on rogue dissociation of triatomic molecules (trimers) into opposite-momentum pairs of atoms and diatomic molecules (dimers) via a photoassociation or Feshbach resonance, we find a superfluid transition to a Bose-Einstein condensate of trimers dressed by atom-dimer Cooper pairs, at a critical temperature in reach of present ultracold technology.
We consider two clouds of ground state alkali atoms in two distinct hyperfine ground states. Each level is far off-resonantly coupled to a Rydberg state, which leads to dressed ground states with a weak admixture of the Rydberg state properties. Due to this admixture, for a proper choice of the Rydberg states, the atoms experience resonant dipole-dipole interactions that induce mechanical forces acting on all atoms within both clouds. This behavior is in contrast to the dynamics predicted for bare dipole-dipole interactions between Rydberg superatoms, where only a single atom per cloud is subj…
Measurement-based quantum computing relies on the rapid creation of large-scale entanglement in a register of stable qubits. Atomic arrays are well suited to store quantum information, and entanglement can be created using highly-excited Rydberg states. Typically, isolating pairs during gate operation is difficult because Rydberg interactions feature long tails at large distances. Here, we engineer distance-selective interactions that are strongly peaked in distance through off-resonant laser coupling of molecular potentials between Rydberg atom pairs. Employing quantum gas microscopy, we veri…
Charge dynamics in an ultra-cold setup involving a laser dressed atom and an ion is studied here. This transfer of charge is enabled through molecular Rydberg states that are accessed via a laser. The character of the charge exchange crucially depends on the coupling between the electronic dynamics and the vibrational motion of the atoms and ion. The molecular Rydberg states are characterized and a criterion for distinguishing coherent and incoherent regimes is formulated. Furthermore the concept is generalized to the many-body setup as the ion effectively propagates through a chain of atoms. …
We present two novel dressed inductive ring trap geometries, ideal for atom interferometry or studies of superfluidity and well-suited to utilisation in atom chip architectures. The design permits ring radii currently only accessible via near-diffraction-limited optical traps, whilst retaining the ultra-smooth magnetic potential afforded by inductive traps. One geometry offers simple parallel implementation of multiple rings, whereas the other geometry permits axial beam-splitting of the torus suitable for whole-ring atom interferometry.
We study the hyperfine spectrum of atoms of $^{87}$Rb dressed by a radio-frequency field, and present experimental results in three different situations: freely falling atoms, atoms trapped in an optical dipole trap and atoms in an adiabatic radio-frequency dressed shell trap. In all cases, we observe several resonant side bands spaced (in frequency) at intervals equal to the dressing frequency, corresponding to transitions enabled by the dressing field. We theoretically explain the main features of the microwave spectrum, using a semi-classical model in the low field limit and the Rotating Wa…
We explore properties of atoms whose magnetic hyperfine sub-levels are coupled by an external magnetic radio frequency (rf) field. We perform a thorough theoretical analysis of this driven system and present a number of systematic approximations which eventually give rise to dressed adiabatic radio frequency potentials. The predictions of this analytical investigation are compared to numerically exact results obtained by a wave packet propagation. We outline the versatility and flexibility of this new class of potentials and demonstrate their potential use to build atom optical elements such a…
We observe the spontaneous evaporation of atoms confined in a bubble-like rf-dressed trap (Zobay and Garraway, 2001). The atoms are confined in a quadrupole magnetic trap and are dressed by a linearly polarized rf field. The evaporation is related to the presence of holes in the trap, at the positions where the rf coupling vanishes, due to its vectorial character. The final temperature results from a competition between residual heating and evaporation efficiency, which is controlled via the height of the holes with respect to the bottom of the trap. The experimental data are modeled by a Mont…
Photoelectron emission from excited states of laser-dressed atomic helium is analyzed with respect to laser intensity-dependent excitation energy shifts and angular distributions. In the two-color XUV (exteme ultra\-violet) -- IR (infrared) measurement, the XUV photon energy is scanned between \SI{20.4}{\electronvolt} and the ionization threshold at \SI{24.6}{\electronvolt}, revealing electric dipole-forbidden transitions for a temporally overlapping IR pulse ($\sim\!\SI{e12}{\watt\per \centi\meter\squared}$). The interpretation of the experimental results is supported by numerically solving t…
Stabilizing important physical quantities to atom-based standards lies at the heart of modern atomic, molecular and optical physics, and is widely applied to the field of precision metrology. Of particular importance is the atom-based microwave field amplitude stabilizer, the so-called atomic candle. Previous atomic candles are realized with atoms in their ground state, and hence suffer from the lack of frequency band tunability and small stabilization bandwidth, severely limiting their development and potential applications. To tackle these limitations, we employ microwave-dressed Rydberg ato…
We develop the research achievement of recent work [M. Gärttner, et.al., Phys. Rev. Letts. 113, 233002 (2014)], in which an anomalous excitation enhancement is observed in a three-level Rydberg-atom ensemble with many-body coherence. In our novel theoretical analysis, this effect is ascribed to the existence of a quasi-dark state as well as its avoided crossings to nearby Rydberg-dressed states. Moreover, we show that with an appropriate control of the optical detuning to the intermediate state, the enhancement can evoke a direct facilitation to atom-light coupling that even breaks through the…
We investigate the transport of excitations through a chain of atoms with non-local dissipation introduced through coupling to additional short-lived states. The system is described by an effective spin-1/2 model where the ratio of the exchange interaction strength to the reservoir coupling strength determines the type of transport, including coherent exciton motion, incoherent hopping and a regime in which an emergent length scale leads to a preferred hopping distance far beyond nearest neighbors. For multiple impurities, the dissipation gives rise to strong nearest-neighbor correlations and …
We propose a method to realize the Frenkel-Kontorova model using an array of Rydberg dressed atoms. Our platform can be used to study this model with a range of realistic interatomic potentials. In particular, we concentrate on two types of interaction potentials: a springlike potential and a repulsive long-range potential. We numerically calculate the phase diagram for such systems and characterize the Aubry-like and commensurate-incommensurate phase transitions. Experimental realizations of this system that are possible to achieve using current technology are discussed.
Comment on "Determining angle of arrival of radio-frequency fields using subwavelength, amplitude-only measurements of standing waves in a Rydberg atom sensor"
We theoretically analyze the interactions and decay rates for atoms dressed by multiple laser fields to strongly interacting Rydberg states using a quantum master equation approach. In this framework a comparison of two-level and three-level Rydberg-dressing schemes is presented. We identify a resonant enhancement of the three-level dressed interaction strength which originates from cooperative multiphoton couplings as well as small distance dependent decay rates. In this regime the soft-core shape of the potential is independent of the sign of the bare Rydberg-Rydberg interaction, while its s…
Methods to manipulate the individual constituents of an ultracold quantum gas mixture are essential tools for a number of applications, for example the direct quantum simulation of impurity physics. We investigate a scheme in which species-selective control is achieved using magnetic potentials dressed with multiple radiofrequencies, exploiting the different Landé g-factors of the constituent atomic species. We describe a mixture dressed with two frequencies, where atoms are confined in harmonic potentials with a controllable degree of overlap between the two atomic species. This is then exten…
We study the dynamics of an atomic Bose-Einstein condensate in an optical lattice in which the electronic groundstate of each atom is weakly coupled to a highly excited Rydberg state by a far off-resonant laser. This dressing induces a switchable effective soft-core interaction between groundstate atoms which, in the lattice, gives rise to on-site as well as long-range interaction terms. Upon switching on the dressing laser the Bose-Einstein condensate undergoes a nontrivial collapse and revival dynamics which can be observed in the interference pattern that is created after a release of the a…
We demonstrate theoretically the existence of a linear dc Stark shift of the individual substates of an alkali atom in its ground state, dressed by a circularly polarized laser field. It arises from the electroweak nuclear anapole moment violating P but not T. It is characterized by the pseudoscalar equal to the mixed product formed with the photon angular momentum and static electric and magnetic fields. We derive the relevant left-right asymmetry with its complete signature in a field configuration selected for a precision measurement with cold atom beams. The 3,3 to 4,3 Cs hyperfine-transit…
Using extreme-ultraviolet attosecond-pulse-trains, we investigate the photoionization dynamics of a Helium atom in the presence of moderately-strong (~10^12 W/cm^2) femtosecond laser pulses. The electronic structure of a laser-dressed atom is traced in real-time through precision measurements of ion-yields and photo-electron angular distributions. Quantum interferences between photo-excitation paths are interpreted using the Floquet formalism. As the laser pulse intensity ramps on femtosecond timescales, we observe transitions between ionization channels mediated by different atomic resonances…
We develop a theoretical model to describe the radio-frequency (rf) induced coupling of a pair of colliding atoms to a Feshbach molecule when a magnetic field arbitrarily far from the Feshbach resonance is modulated in time. We use the dressed atom picture, and show that the coupling strength in presence of rf is equal to the Feshbach coupling strength multiplied by the square of a Bessel function. The argument of this function is equal to the ratio of the atomic rf Rabi frequency to the rf frequency. We experimentally demonstrate this law by measuring the rate of rf-association of molecules u…
We study the spectroscopy of atoms dressed by a resonant radiofrequency (RF) field inside an inhomogeneous magnetic field and confined in the resulting adiabatic potential. The spectroscopic probe is a second, weak, RF field. The observed line shape is related to the temperature of the trapped cloud. We demonstrate evaporative cooling of the RF-dressed atoms by sweeping the frequency of the second RF field around the Rabi frequency of the dressing field.
We propose a flexible and robust scheme to create closed quasi-one dimensional guides for ultra-cold atoms through the dressing of hyperfine sub-levels of the atomic ground state. The dressing field is spatially modulated by inductive effects over a micro-engineered conducting loop, freeing the trapping region from leading wires in its proximity. We show that arrays of connected ring traps can also be created by carefully designing the shape of the conducting loop. We report on characteristics of the trap and mechanisms that limit the range of parameters available for experimental implementati…
We study the spectral signatures and coherence properties of radiofrequency dressed hyperfine Zeeman sub-levels of 87Rb. Experimentally, we engineer combinations of static and RF magnetic fields to modify the response of the atomic spin states to environmental magnetic field noise. We demonstrate analytically and experimentally the existence of 'magic' dressing conditions where decoherence due to electromagnetic field noise is strongly suppressed. Building upon this result, we propose a bi-chromatic dressing configuration that reduces the global sensitivity of the atomic ground states to low-f…
X-ray refraction and absorption by neon atoms under the influence of an 800 nm laser with an intensity of 10^13 W/cm^2 is investigated. For this purpose, we use an ab initio theory suitable for optical strong-field problems. Its results are interpreted in terms of a three-level model. On the Ne 1s --> 3p resonance, we find electromagnetically induced transparency (EIT) for x rays. Our work opens novel perspectives for ultrafast x-ray pulse shaping.
Cavity electromagnetically induced transparency in a coherently prepared cavity-atom system is manifested as a narrow transmission peak of a weak probe laser coupled into the cavity mode. We show that with a resonant pump laser coupling the cavity-confined four-level atoms from free space, the narrow transmission peak of the cavity EIT is split into two peaks. The two peaks represent the dressed intra-cavity dark states and have a frequency separation approximately equal to the Rabi frequency of the free-space pump laser. We observed experimentally the dressed intra-cavity dark states in cold …
This paper introduces and reviews light forces, atom cooling and atom trapping. The emphasis is on the physics of the basic processes. In discussing conservative forces the semi-classical dressed states are used rather than the usual quantized field dressed states.
