Ac Stark Shift Research Articles

Ac Stark shift measurements of the clock transition in cold Cs atoms: Scalar and tensor light shifts of theD2transition

The ac Stark shift, or light shift, is a physical phenomenon that plays a fundamental role in many applications ranging from basic atomic physics to applied quantum electronics. Here, we discuss experiments testing light-shift theory in a cold-atom cesium fountain clock for the Cs ${D}_{2}$ transition (i.e., $6\phantom{\rule{0.28em}{0ex}}{}^{2}{S}_{1/2}\ensuremath{\rightarrow}6\phantom{\rule{0.28em}{0ex}}{}^{2}{P}_{3/2}$ at 852 nm). Cold-atom fountains represent a nearly ideal system for the study of light shifts: (1) The atoms can be perturbed by a field of arbitrary character (e.g., coherent field or nonclassical field); (2) there are no trapping fields to complicate data interpretation; (3) the probed atoms are essentially motionless in their center-of-mass reference frame, $T$ \ensuremath{\sim} 1 \ensuremath{\mu}K; and (4) the atoms are in an essentially collisionless environment. Moreover, in the present work the resolution of the Cs excited-state hyperfine splittings implies that the ${D}_{2}$ ac Stark shift contains a nonzero tensor polarizability contribution, which does not appear in vapor phase experiments due to Doppler broadening. Here, we test the linearity of the ac Stark shift with field intensity, and measure the light shift as a function of field frequency, generating a ``light-shift curve.'' We have improved on the previous best test of theory by a factor of 2, and after subtracting the theoretical scalar light shift from the experimental light-shift curves, we have isolated and tested the tensor light shift for an alkali ${D}_{2}$ transition.

Trapped ion 88Sr+ optical clock systematic uncertainties - AC Stark shift determination

A recent comparison between two trapped-ion 88Sr+ optical clocks at the UK. National Physical Laboratory demonstrated agreement to 4 parts in 1017. One of the uncertainty contributions to the optical clock absolute frequency arises from the blackbody radiation shift which in turn depends on uncertainty in the knowledge of the differential polarisability between the two clocks states. Whilst a recent NRC measurement has determined the DC differential polarisability to high accuracy, there has been no experimental verification to date of the dynamic correction to the DC Stark shift. We report a measurement of the scalar AC Stark shift at 1064 nm with measurements planned at other wavelengths. Our preliminary result using a fibre laser at 1064 nm agrees with calculated values to within ∼3%.

Three-photon process for producing a degenerate gas of metastable alkaline-earth-metal atoms

We present a method for creating a quantum degenerate gas of metastable alkaline-earth atoms. This has yet to be achieved due to inelastic collisions that limit evaporative cooling in the metastable states. Quantum degenerate samples prepared in the $^{1}S_{0}$ ground state can be rapidly transferred to either the $^{3}P_{2}$ or $^{3}P_{0}$ state via a coherent 3-photon process. Numerical integration of the density matrix evolution for the fine structure of bosonic alkaline-earth atoms shows that transfer efficiencies of $\simeq90\%$ can be achieved with experimentally feasible laser parameters in both Sr and Yb. Importantly, the 3-photon process can be set up such that it imparts no net momentum to the degenerate gas during the excitation, which will allow for studies of metastable samples outside the Lamb-Dicke regime. We discuss several experimental challenges to successfully realizing our scheme, including the minimization of differential AC Stark shifts between the four states connected by the 3-photon transition.

Beam propagation near the dispersionless wavelength at 790 nm in rubidium

Between any two resonance lines for an atomic medium there exists a dispersionless wavelength where the ac Stark shift from the two resonances cancel and the real part of the resonant susceptibility is 0. We experimentally demonstrate the effects of this wavelength in a pump-probe experiment in high-density atomic vapor. A strong pump field excites the medium, in which we counterpropagate a broadband probe field. In a long cell, only at the dispersionless wavelength will scattering and self-focusing or defocusing not cause attenuation, allowing a spectrometer to read off the dispersionless wavelength. We perform a propagation experiment that shows the passband centered around the 790-nm dispersionless wavelength between the ${D}_{1}$ and the ${D}_{2}$ lines of rubidium.

A simple 2 W continuous-wave laser system for trapping ultracold metastable helium atoms at the 319.8 nm magic wavelength

High precision spectroscopy on the $2 \ ^3 S \rightarrow 2 \ ^1 S$ transition is possible in ultracold optically trapped helium but the accuracy is limited by the ac-Stark shift induced by the optical dipole trap. To overcome this problem, we have built a trapping laser system at the predicted magic wavelength of 319.8 nm. Our system is based on frequency conversion using commercially available components and produces over 2 W of power at this wavelength. With this system, we show trapping of ultracold atoms, both thermal ($\sim0.2 \ \mathrm{\mu K}$) and in a Bose-Einstein condensate, with a trap lifetime of several seconds, mainly limited by off-resonant scattering.

Precision test of the ac Stark shift in a rubidium atomic vapor

The ac Stark shift (also known as the ``light shift'') is one of the most important physical processes that arises in precision spectroscopy, affecting the basic understanding of field-matter interactions, measurements of fundamental constants, and even the atomic clocks onboard GPS satellites. Although the theory of the ac Stark shift was fully developed by the 1960s and 1970s, precision tests of theory have, for the most part, been few. Taking advantage of recent developments in atomic clock technology, specifically the pulsed approach to atomic signal generation, which allows frequency measurements with a resolution of $\ensuremath{\sim}{10}^{\ensuremath{-}15}$, we demonstrate a methodology for measuring the ac Stark shift. Here, we report results from a precision examination of the ac Stark shift in a vapor phase system, examining the resonant frequency of the $^{87}\text{Rb}$ 0-0 hyperfine transition for a perturbing laser tuned over a broad optical frequency range (18 GHz) around the ${D}_{1}$ absorption resonance. Over the full frequency range the agreement between semiclassical theory and experiment is very good (better than $5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}2}$), and in our experiments we test both the frequency dependence of the scalar and tensor components of the light shift.

Precision measurement of theRb87tune-out wavelength in the hyperfine ground stateF=1at 790 nm

We report on a precision measurement of the $D$ line tune-out wavelength of $^{87}$Rubidium in the hyperfine ground state $|F=1, m_F=0,\pm1 \rangle$ manifold at 790 nm, where the scalar ac Stark shifts of the $D_1$ and the $D_2$ lines cancel. This wavelength is sensitive to usually neglected contributions from vector and tensor ac Stark shifts, transitions to higher principle quantum numbers, and core electrons. The ac Stark shift is probed by Kapitza-Dirac scattering of a Rubidium Bose-Einstein condensate in a one-dimensional optical lattice in free space and controlled magnetic environment. The tune-out wavelength of the magnetically insensitive $m_F=0$ state was determined to 790.01858(23) nm with sub pm accuracy. An in situ absolute polarization, and magnetic background field measurement is performed by employing the ac vector Stark shift for the $m_F=\pm 1$ states. Comparing our findings to theory, we get quantitative insight into atomic physics beyond commonly used two-level atom approximations or the neglect of inner shell contributions.

Phase-Stable Free-Space Optical Lattices for Trapped Ions.

We demonstrate control of the absolute phase of an optical lattice with respect to a single trapped ion. The lattice is generated by off-resonant free-space laser beams, and we actively stabilize its phase by measuring its ac-Stark shift on a trapped ion. The ion is localized within the standing wave to better than 2% of its period. The locked lattice allows us to apply displacement operations via resonant optical forces with a controlled direction in phase space. Moreover, we observe the lattice-induced phase evolution of spin superposition states in order to analyze the relevant decoherence mechanisms. Finally, we employ lattice-induced phase shifts for inferring the variation of the ion position over the 157 μm range along the trap axis at accuracies of better than 6nm.

852-nm triggered single-photon source based on trapping and manipulation of a single cesium atom confined in a microscopic optical dipole trap

Single-atom-based single-photon source has several advantages, such as narrow bandwidth, wavelength matching with the absorption line of the same atomic ensemble, and insensitivity to the environment disturbing, and it is very important not only for basic researches in quantum optic field but also for applications in quantum information processing. In this paper, we report the generation of a 10-MHz-repetition-rate triggered single-photon source at 852 nm based on a trapped single cesium atom in a far-off-resonance microscopic optical dipole trap (FORT). To generate an optical dipole trap, a far-red-detuned 1064 nm laser beam is tightly focused by using a high numerical aperture lens, a typical trap depth is 2 mK and trap waist is 2.3 m. To obtain a maximum probability of pulsed excitation, the frequency of the pulsed laser should be resonant with the atomic energy levels and the trapped single atom must be excited with a -pulse. However, the interaction between the FORT laser and the atoms causes AC Stark shifts of the atomic energy levels. Thus, in order to demonstrate the resonant pulsed excitation, it is important to calculate and measure the shift of 6S1/2|Fg=4,mF=+4-6P3/2|Fe=5,mF=+5 cyclical transition in the FORT. For a two-level system, the probability of pulsed excitation can be described by Rabi oscillations with a characteristic Rabi frequency . With an optimized time sequence, we experimentally demonstrate the Rabi oscillation between the ground state and the excited state, and the peak power of -pulse laser is about 1.25 mW. We also measure the temporal envelope of single photons after a -pulse excitation. A gated pulsed excitation and cooling technique are used to reduce the possibility that atoms are heated by -pulse laser. The typical trapping lifetime of single cesium atom is extended from~108 ups to~2536 ms. The corresponding number of excitations is improved from 108 to 360000. The second-order intensity correlations of the emitted single-photon are characterized by implementing Hanbury Brown-Twiss setup. The statistics shows a strong anti-bunching with a value of 0.09 for the second-order correlation at zero delay. In the future, we will perform a Hong-Ou-Mandel two-photon interference experiment to analyze the indistinguishability of the single photons. We will also trap single atoms in a magic-wavelength optical dipole trap where the ground and the excited states have the same shift.

Nonlinear microwave photon occupancy of a driven resonator strongly coupled to a transmon qubit

We measure photon-occupancy in a thin-film superconducting lumped element resonator coupled to a transmon qubit at 20$\,$mK and find a nonlinear dependence on the applied microwave power. The transmon-resonator system was operated in the strong dispersive regime, where the ac Stark shift ($2\chi$) due to a single microwave photon present in the resonator was larger than the linewidth ($\Gamma$) of the qubit transition. When the resonator was coherently driven at $5.474325\,$GHz, the transition spectrum of the transmon at $4.982\,$GHz revealed well-resolved peaks, each corresponding to an individual photon number-state of the resonator. From the relative peak-heights we obtain the occupancy of the photon-states and the average photon-occupancy $\bar{n}$ of the resonator. We observed a nonlinear variation of $\bar{n}$ with the applied drive power $P_{rf}$ for $\bar{n} < 5$ and compare our results to numerical simulations of the system-bath master equation in the steady state, as well as to a semi-classical model for the resonator that includes the Jaynes-Cummings interaction between the transmon and the resonator. We find good quantitative agreement using both models and analysis reveals that the nonlinear behavior is principally due to shifts in the resonant frequency caused by a qubit-induced Jaynes-Cummings nonlinearity.

Species-selective lattice launch for precision atom interferometry

Long-baseline precision tests based on atom interferometry require drastic control over the initial external degrees of freedom of atomic ensembles to reduce systematic effects. The use of optical lattices (OLs) is a highly accurate method to manipulate atomic states in position and momentum allowing excellent control of the launch in atomic fountains. The simultaneous lattice launch of two atomic species, as required in a quantum test of the equivalence principle, is however problematic due to crosstalk effects. In this article, we propose to selectively address two species of alkalines by applying two OLs at or close to magic-zero wavelengths of the atoms. The proposed scheme applies in general for a pair of species with a vastly different ac Stark shift to a laser wavelength. We illustrate the principle by studying a fountain launch of condensed ensembles of 87Rb and 41K initially co-located. Numerical simulations confirm the fidelity of our scheme up to few nm and nm s−1 in inter-species differential position and velocity, respectively. This result is a pre-requisite for the next performance level in precision tests.

Analysis of thermal radiation in ion traps for optical frequency standards

In many of the high-precision optical frequency standards with trapped atoms or ions that are under development to date, the ac Stark shift induced by thermal radiation leads to a major contribution to the systematic uncertainty. We present an analysis of the inhomogeneous thermal environment experienced by ions in various types of ion traps. Finite element models which allow the determination of the temperature of the trap structure and the temperature of the radiation were developed for five ion trap designs, including operational traps at PTB and NPL and further optimized designs. Models were refined based on comparison with infrared camera measurement until an agreement of better than 10% of the measured temperature rise at critical test points was reached. The effective temperature rises of the radiation seen by the ion range from 0.8 K to 2.1 K at standard working conditions. The corresponding fractional frequency shift uncertainties resulting from the uncertainty in temperature are in the 10−18 range for optical clocks based on the Sr+ and Yb+ E2 transitions, and even lower for Yb+ E3, In+ and Al+. Issues critical for heating of the trap structure and its predictability were identified and design recommendations developed.

Magic wavelength for the hydrogen1S−2Stransition

The magic wavelength for an optical lattice for hydrogen atoms that cancels the lowest order AC Stark shift of the 1S-2S transition is calculated to be 513 nm. The magnitude of AC Stark shift $\Delta E=-1.19$ kHz/(10kW/cm$^2$) and the slope $d\Delta E/d\nu = -27.7$ Hz/(GHz $\cdot$ 10 kW/cm$^2$) at the magic wavelength suggests that a stable and narrow linewidth trapping laser is necessary to achieve a deep enough optical lattice to confine hydrogen atoms in a way that gives a small enough light shift for the precision spectroscopy of the 1S-2S transition.

Analytical studies on the coherent AC Stark effect of an open λ-type drive-probe system

The Doppler-free absorptive lineshape and its physical parameters are analytically formulated for an open λ-type coherently prepared drive-probe system. The individual contribution of drive and probe fields on AC Stark splitting is demonstrated through power broadened lineshape. We exhibit the sharpness and asymmetric nature of Stark splitting for probe field induced quantum coherence and atomic coherence. The coherent linear Stark shift due to probe and drive fields is classified by means of various physical controlling parameters. It is shown that the direction of the AC Stark shift towards red or blue region can be controlled via probe field induced quantum coherence.

The ac Stark shifts of the terahertz clock transitions of barium**Project supported by the Science Fund from the Shaanxi Provincial Education Department, China (Grant No. 14JK1402).

Wavelength-dependent AC Stark shifts and magic wavelengths of the terahertz clock transitions between the metastable triplet states 6s5d 3D1 and 6s5d 3D2 are investigated with considering the optical lattice trapping of barium atoms with the linearly polarized laser. The trap depths and the slopes of light shift difference with distinct magic wavelengths of the optical lattices are also discussed in detail. Several potentially suitable working points for the optical lattice trapping laser are recommended and selected from these magic wavelengths.

Correlation-based entanglement criterion in bipartite multiboson systems

We describe a criterion for the detection of entanglement between two multi-boson systems. The criterion is based on calculating correlations of Gell-Mann matrices with a fixed boson number on each subsystem. This applies naturally to systems such as two entangled spinor Bose-Einstein condensates. We apply our criterion to several experimentally motivated examples, such as an $ S^z S^z $ entangled BECs, ac Stark shift induced two-mode squeezed BECs, and photons under parametric down conversion. We find that entanglement can be detected for all parameter regions for the most general criterion. Alternative criteria based on a similar formalism are also discussed together with their merits.

Rydberg-blockade controlled-not gate and entanglement in a two-dimensional array of neutral-atom qubits

We present experimental results on two-qubit Rydberg blockade quantum gates and entanglement in a two-dimensional qubit array. Without post selection against atom loss we achieve a Bell state fidelity of $0.73\pm 0.05$, the highest value reported to date. The experiments are performed in an array of single Cs atom qubits with a site to site spacing of $3.8 ~ \mu\rm m$. Using the standard protocol for a Rydberg blockade C$_Z$ gate together with single qubit operations we create Bell states and measure their fidelity using parity oscillations. We analyze the role of AC Stark shifts that occur when using two-photon Rydberg excitation and show how to tune experimental conditions for optimal gate fidelity.

Bichromatic state-insensitive trapping of caesium atoms

State-insensitive dipole trapping of multilevel atoms can be achieved by an appropriate choice of the wavelength of the trapping laser, so that the interaction with the different transitions results in equal AC Stark shifts for the ground and excited states of interest. However, this approach is severely limited by the availability of coherent sources at the required wavelength and of appropriate power. This work investigates state-insensitive trapping of caesium atoms for which the required wavelength of 935.6 nm is inconvenient in terms of experimental realization. Bichromatic state-insensitive trapping is proposed to overcome the lack of suitable laser sources. We first consider pairs of laser wavelengths in the ratio 1:2 and 1:3, as obtained via second- and third-harmonic generation. We found that the wavelength combinations 931.8–1863.6 nm and 927.5–2782.5 nm are suitable for state-insensitive trapping of caesium atoms. In addition, we examine bichromatic state-insensitive trapping produced by pairs of laser wavelengths corresponding to currently available high-power lasers. These wavelength pairs were found to be in the range of 585–588 nm and 623–629 for one laser and 1064–1080 nm for the other.

Dressing Effects in the Attosecond Transient Absorption Spectra of Doubly-Excited States in Helium

SynopsisStrong-field manipulation of autoionizing states is a crucial aspect of electronic quantum control. Recent measurements of the attosecond transient absorption spectrum (ATAS) of helium dressed by a few-cycle visible pulse [C. Ott et al, Nature 516, 374 (2014)] provide evidence of the inversion of Fano profiles. With the support of accurate ab-initio calculations that reproduce the results of the latter experiment, here we investigate the new physics that arise from ATAS when the laser intensity is increased. In particular, we show that (i) previously unnoticed signatures of the dark 2p2 1S doubly excited state are observed in the experimental spectrum, (ii) inversion of Fano profiles is predicted to be periodic in the laser intensity, and (iii) the ac-Stark shift of the higher terms in the sp+2, n autoionizing series exceeds the ponderomotive energy, which is the result of a genuine two-electron contribution to the polarization of the excited atom.

Analytical treatment of the continuous wave driving of a two-level atom without making the rotating wave approximation

In a straightforward manner, we utilize Floquet theory and adiabatic elimination to derive an analytic expression for a monochromatically driven two-level atom, without making the rotating wave approximation. We show that the counter-rotating terms dropped in the rotating wave approximation are responsible for three major effects. First an ac-Stark phase shift of the driven transition, second increased excited state population from far-detuned driving of the Lorentzian line, and third extra frequencies in the population dynamics that result in “wiggles.” The analytic result agrees well with numerical simultations over a wide range of parameters.