Ac Stark Shift Research Articles

Rydberg excitation through detuned microwave transition in rubidium

We study the excitation of Rydberg states in warm rubidium vapor. Using an inverted wavelength excitation scheme, we observe the effect of microwave coupling between Rydberg states through electromagnetically induced transparency. We observe AC stark shifts of the Rydberg states from the microwave coupling, and demonstrate detuned excitation to a secondary Rydberg state. These results show flexibility in the excitation process and state selection necessary for a variety of wave-mixing processes using Rydberg states.

Excitation of 87Rb Rydberg atoms to nS and nD states (n≤68) via an optical nanofiber

Cold Rydberg atoms are a promising platform for quantum technologies, and combining them with optical waveguides has the potential to create robust quantum information devices. Here, we experimentally observe the excitation of cold rubidium atoms to a large range of Rydberg S and D states through interaction with the evanescent field of an optical nanofiber. We develop a theoretical model to account for experimental phenomena present such as the AC Stark shifts and the Casimir–Polder interaction. This work strengthens the knowledge of Rydberg atom interactions with optical nanofibers and is a critical step toward the implementation of all-fiber quantum networks and waveguide quantum electrodynamics (QED) systems using highly excited atoms.

Excitation of 87Rb Rydberg atoms to nS and nD states (n≤68) via an optical nanofiber

Cold Rydberg atoms are a promising platform for quantum technologies, and combining them with optical waveguides has the potential to create robust quantum information devices. Here, we experimentally observe the excitation of cold rubidium atoms to a large range of Rydberg S and D states through interaction with the evanescent field of an optical nanofiber. We develop a theoretical model to account for experimental phenomena present such as the AC Stark shifts and the Casimir–Polder interaction. This work strengthens the knowledge of Rydberg atom interactions with optical nanofibers and is a critical step toward the implementation of all-fiber quantum networks and waveguide quantum electrodynamics (QED) systems using highly excited atoms.

174Yb+–113Cd+ sympathetic-cooling bi-species Coulomb crystal applied to microwave frequency standard

We reported the realization of a 174Yb+–113Cd+ bi-species Coulomb crystal comprising 174Yb+, a heavier ion, as coolant and verified the potential of applying a coolant ion with a greater mass than the clock ion to sympathetically cooled microwave frequency standard. The two species of massive ions stably trapped in a Paul trap make up this large two-component crystal. The 113Cd+ ions are trapped in the center, which reduces considerably RF heating and excess micro-motion to which the 113Cd+ ions are subjected. Under this scheme, the uncertainty due to the second-order Doppler effect is reduced to 5×10−16, which represents an order of magnitude improvement over sympathetic cooled 40Ca+–113Cd+ crystal. The second-order Zeeman frequency shift, which contributes the largest term of the systematic frequency shifts to the microwave ion frequency standard, is estimated to be as low as 7.133×10−13 corresponding to the low value of the operating magnetic field. The relevant AC Stark shift uncertainty is estimated to be 4×10−19. These results demonstrate that using a heavier coolant ion is far superior and confirm the feasibility of a sympathetic-cooled cadmium-ion microwave clock system employing a 174Yb+–113Cd+ bicrystal.

Influence of ac Stark shift on below-threshold harmonic generation of H molecular ions in intense laser fields

The effects of laser-induced ac Stark shift on the high-order harmonic generation below the ionization threshold of H molecular ions are investigated. The results show that several sub-peak harmonics generated in the vicinity of odd harmonics are clearly observed. Combined with the synchrosqueezing transform of the quantum time-frequency spectrum and a two-state model, we confirm that the transition between the first excited state related to ac Stark-shift and the ground state contributes to the sub-peak harmonics generation. In addition, we find some fine oscillatory structures of the sub-peak harmonic due to spectral interference. The sub-peak harmonics generation and spectral oscillations can be controlled by the laser intensity and the pulse duration. Our study provides a new alternative way to measure the energy difference of ac Stark shift between the excited state and the ground state of atoms and molecules in intense laser fields.

Escaping Detrimental Interactions with Microwave-Dressed Transmon Qubits

Superconducting transmon qubits with fixed frequencies are widely used in many applications due to their advantages of better coherence and less control lines compared to the frequency tunable qubits. However, any uncontrolled interactions with the qubits such as the two-level systems could lead to adverse impacts, degrading the qubit coherence and inducing crosstalk. To mitigate the detrimental effect from uncontrolled interactions between qubits and defect modes in fixed-frequency transmon qubits, we propose and demonstrate an active approach using an off-resonance microwave drive to dress the qubit and to induce the ac-Stark shift on the qubit frequency. We show experimentally that the qubit frequency can be tuned well away from the defect mode so that the impact on qubit coherence is greatly reduced while maintaining the universal controls of the qubit initialization, readout, and single-qubit gate operations. Our approach provides an effective way for tuning the qubit frequency and suppressing the detrimental effect from the defect modes that happen to be located close to the qubit frequency.

Possible Improvements in the Precision of the Atom-interferometric Equivalence Principle Test by Reducing AC Stark Shift Uncertainty

We discussed possible improvement methods for a dual-species atom interferometry test of the weak equivalence principle (WEP) at the 10^(-12) level. The original research tested the WEP by comparing the acceleration difference of the free-fallen rubidium isotopes atom clouds. Based on the percent uncertainty presented from this test, AC stark shift is the most significant obstacle to improving precision. This article will discuss a precision-improving method to the original test by suppressing the background AC stark shift by centering the interferometry lasers to their "magic frequency." The expected improved precision of the uncertainty level is below the 10^(-18) level. Due to the limitation of instruments, we have yet to test this improving method in the actual measurement. Still, we analyzed the possible difficulties in practical usage and discussed solving strategies that correspond to the problems.

Multistate interferometric measurement of the nonlinear ac Stark shift

We demonstrate measurement of quadratic AC Stark shifts between Zeeman sublevels in an $^{87}$Rb Bose--Einstein condensate using a multi-state atomic interferometer. The interferometer can detect a quadratic shift without being affected by relatively large state-independent shifts, thereby improving the measurement precision. We measure quadratic shifts in the total spin $F = 2$ state due to the light being near-resonant to the D$_1$ line. The agreement between the measured and theoretical detuning dependences of the quadratic shifts confirms the validity of the measurement. We also present results on the suppression of nonlinear spin evolution using near-resonant dual-color light pulses with opposite quadratic shifts.

Direct calibration of laser intensity via Ramsey interferometry for cold atom imaging.

A majority of ultracold atom experiments utilize resonant absorption imaging techniques to obtain the atomic density. To make well-controlled quantitative measurements, the optical intensity of the probe beam must be precisely calibrated in units of the atomic saturation intensity Isat. In quantum gas experiments, the atomic sample is enclosed in an ultra-high vacuum system that introduces loss and limits optical access; this precludes a direct determination of the intensity. Here, we use quantum coherence to create a robust technique for measuring the probe beam intensity in units of Isat via Ramsey interferometry. Our technique characterizes the ac Stark shift of the atomic levels due to an off-resonant probe beam. Furthermore, this technique gives access to the spatial variation of the probe intensity at the location of the atomic cloud. By directly measuring the probe intensity just before the imaging sensor our method in addition yields a direct calibration of imaging system losses as well as the quantum efficiency of the sensor.

Control of an Atomic Quadrupole Transition in a Phase-Stable Standing Wave.

Using a single calcium ion confined in a surface-electrode trap, we study the interaction of electric quadrupole transitions with a passively phase-stable optical standing wave field sourced by photonics integrated within the trap. We characterize the optical fields through spatial mapping of the Rabi frequencies of both carrier and motional sideband transitions as well as ac Stark shifts. Our measurements demonstrate the ability to engineer favorable combinations of sideband and carrier Rabi frequency as well as ac Stark shifts for specific tasks in quantum state control and metrology.

Coherence-preserving cooling of nuclear-spin qubits in a weak magnetic field

Nuclear-spin memories of divalent neutral atoms can allow spin-preserving resolved-sideband cooling in a strong magnetic field [I. Reichenbach and I. H. Deutsch, Phys. Rev. Lett. 99, 123001 (2007)]. We present a theory for cooling $^{87}\mathrm{Sr}$ nuclear-spin qubits in a weak magnetic field. The theory depends on laser excitation of $5s5p\phantom{\rule{0.16em}{0ex}}^{3}P_{1}$ to a nearby state which results in ${m}_{J}$-dependent AC Stark shifts large compared to the hyperfine interaction. This effectively suppresses the nuclear-spin mixing due to the hyperfine interaction. Sideband cooling via the clock state quenched by the AC Stark-shifted $^{3}P_{1}$ state leads to nuclear-spin-preserving spontaneous emission back to the ground state. More than being compatible with low magnetic fields, the theory is applicable when the nuclear-spin qubits are defined by the two lowest Zeeman substates.

Probe-Field-Ellipticity-Induced Shift in an Atomic Clock

We investigate near-resonant ac-Stark shifts for optical atomic clocks, which can also be interpreted as a special class of line-pulling effects due to the Zeeman structure of atomic levels split in a dc magnetic field. This shift can arise due to residual ellipticity in the polarization of the probe field and uncertainty in the magnetic field orientation. Such a shift can have an arbitrary sign and, for some experimental conditions, can reach a fractional value of the order of ${10}^{\ensuremath{-}18}$--${10}^{\ensuremath{-}19}$, i.e., it is not negligible. Thus, it should be taken into account in the uncertainty budgets for modern ultraprecise atomic clocks. In addition, it is shown that when using hyper-Ramsey spectroscopy, this shift can be reduced to a level much lower than ${10}^{\ensuremath{-}19}$.

Theoretical analysis of polarization-angle-dependent magic-wavelength optical dipole trap of Cs atoms

Laser cooling and trapping of neutral atoms is of great significance for studying the physical and chemical properties of atoms. To further realize the spatial localization of atoms, optical dipole trap (ODT) was proposed to manipulate individual atoms, ions or molecules and has become an increasingly important technique in the field of cold atomic physics and quantum optics. To eliminate the differential light shift of transitions between atomic states, ODT can be turned off during excitation/radiation. However, it will shorten the trap lifetime of the atom and reduce the repetition rate of the single photon. The AC stark shift can be eliminated experimentally by constructing blue-detuned dark ODT, but the micron-level dark ODT usually requires more complex experimental equipment and is not easy to operate. Therefore, magic-wavelength ODT was constructed to realize that the transition frequency of photons between atomic states is the same as in free space. When the trapping laser makes the differential light shift of the transition between the two atomic states zero, the laser wavelength is called the magic wavelength. The magic-wavelength ODT can eliminate the differential light shift of the transition between atoms, improve the repetition rate of the experimental sequence and weaken the atomic decoherence. In recent years, it has become a powerful tool for manipulating cold atoms, especially for coherently manipulating the atomic inner states. In the present work, with the theory of multi-level model, we calculate the dynamic electric polarizability of the 6S<sub>1/2</sub> ground state and the 6P<sub>3/2</sub> excited state connecting the D2 line of cesium atom in a range of 800–1000 nm, and obtain the magic wavelength of the optical trapping laser to trap the ground state and the excited state. Since the polarizability of atomic states with angular momentum greater than 0.5 is very sensitive to the polarization angle, the polarization-angle-dependent magic wavelength and the corresponding magic polarizability are analyzed by taking the linearly-polarized trapping laser for example. The magic polarization angle is 54.7° and the magic wavelength at this angle are 886.4315 and 934.0641 nm, respectively. The robustness of the magic conditions and the feasibility of the experimental operation are further analyzed.

Effect of nonresonant states in near-resonant two-photon ionization of hydrogen

By numerically solving the three-dimensional time-dependent Schr\"odinger equation, two-photon ionization of hydrogen is investigated at the near-resonant frequencies of the $1s\text{\ensuremath{-}}2p$ transition. Due to the Rabi oscillations between the $1s$ and $2p$ states, the photoelectron energy spectra exhibit the Autler-Townes (AT) doublets and we focus on the energy spacing and the asymmetry of the doublets. Our results show that the laser frequency for the minimum energy spacing of AT doublets locates at the resonant frequency of the ac-stark-shifted states, while the symmetry of the AT doublets is affected both by the ac-stark shift and the nonresonant ionization pathway. Developing the minimal three-state model including all of the nonresonant (nonessential) states, the effects of the ac-stark shift and the nonresonant ionization pathway on the AT doublets due to the nonresonant states are identified. Furthermore, due to the nonresonant ionization pathway, the photoelectron angular distributions are distinctly different for the lower- and higher-energy peaks in the AT doublets and these angular distributions sensitively depend on the laser intensity and pulse duration. These results are well reproduced by our minimal three-state model.

High-fidelity qutrit entangling gates for superconducting circuits

Ternary quantum information processing in superconducting devices poses a promising alternative to its more popular binary counterpart through larger, more connected computational spaces and proposed advantages in quantum simulation and error correction. Although generally operated as qubits, transmons have readily addressable higher levels, making them natural candidates for operation as quantum three-level systems (qutrits). Recent works in transmon devices have realized high fidelity single qutrit operation. Nonetheless, effectively engineering a high-fidelity two-qutrit entanglement remains a central challenge for realizing qutrit processing in a transmon device. In this work, we apply the differential AC Stark shift to implement a flexible, microwave-activated, and dynamic cross-Kerr entanglement between two fixed-frequency transmon qutrits, expanding on work performed for the ZZ interaction with transmon qubits. We then use this interaction to engineer efficient, high-fidelity qutrit CZ† and CZ gates, with estimated process fidelities of 97.3(1)% and 95.2(3)% respectively, a significant step forward for operating qutrits on a multi-transmon device.

Temperature-shift-suppression scheme for two-photon two-color rubidium vapor clocks

We propose a scheme for interrogating a warm rubidium vapor using two different clock lasers. Performance wise, this approach is distinctly different from the recently proposed two-color two-photon rubidium clocks as our scheme does not trade off the ac Stark suppression against an increased sensitivity to the cell temperature or pressure. Instead, our approach compensates both the ac Stark shift and the temperature and pressure-induced frequency shifts. The proposed scheme also makes use of the modulation transfer technique, which enables a two orders of magnitude increase in the signal-to-noise ratio compared to traditional clocks that rely on fluorescence measurements.

Detecting topological phase transitions in a double kicked quantum rotor

We present a concrete theoretical proposal for detecting topological phase transitions in double kicked atom-optics kicked rotors with internal spin-1/2 degree of freedom. The implementation utilizes a kicked Bose-Einstein condensate evolving in one-dimensional momentum space. To reduce influence of atom loss and phase decoherence we aim to keep experimental durations short while maintaining a resonant experimental protocol. Experimental limitations induced by phase noise, quasimomentum distributions, symmetries, and the AC-Stark shift are considered. Our results thus suggest a feasible and optimized procedure for observing topological phase transitions in quantum kicked rotors.

Sensitivity enhancement of far-detuned RF field sensing based on Rydberg atoms dressed by a near-resonant RF field.

Rydberg-atom electrometers promise traceable standards for RF electrometry by enabling stable and uniform measurement. In this Letter, we propose an approach to increase the sensitivity of the Rydberg-atom electrometer for far-detuned RF field sensing. The key physical mechanism is the addition of a new ingredient-a local RF field near-resonant with a Rydberg transition-so that the far-detuned field can be detected by the shift of an Autler-Townes (AT) splitting peak, which can be dozens of times larger than the AC Stark shift of the electromagnetic induced transparency (EIT) signal without the near-resonant field. The method enables us to measure far-detuned fields with higher sensitivities, including sub-GHz RF fields (even DC electric fields) which are rarely involved in the existing sensitivity enhancement methods.

Controlled-phase gate by dynamic coupling of photons to a two-level emitter

We propose an architecture for achieving high-fidelity deterministic quantum logic gates on dual-rail encoded photonic qubits by letting photons interact with a two-level emitter (TLE) inside an optical cavity. The photon wave packets that define the qubit are preserved after the interaction due to a quantum control process that actively loads and unloads the photons from the cavity and dynamically alters their effective coupling to the TLE. The controls rely on nonlinear wave mixing between cavity modes enhanced by strong externally modulated electromagnetic fields or on AC Stark shifts of the TLE transition energy. We numerically investigate the effect of imperfections in terms of loss and dephasing of the TLE as well as control field miscalibration. Our results suggest that III-V quantum dots in GaAs membranes is a promising platform for photonic quantum information processing.

Hyperfine coupling constants of the cesium 7D5/2 state measured up to the octupole term.

We report the measurement of hyperfine splitting (HFS) in the 7D5/2 state of 133Cs using high-resolution Doppler-free two-photon spectroscopy enabled by precise frequency scans using an acousto-optic modulator (AOM). All six hyperfine levels are resolved in our spectra. We determine the hyperfine coupling constants A = -1.70867(62) MHz and B = 0.050(14) MHz which represent an over 20-times improvement in the precision of both A and B. Moreover, our measurement is sufficiently precise to put bounds on the value of the magnetic octupole coupling constant C = 0.4(1.4) kHz for the 7D5/2 state. We additionally report the measurement of the ac Stark shift [-46 ± 4 Hz/(W/cm2)], collisional shift, and pressure broadening which are important for optical frequency standards based on the 6S1/2 → 7D5/2 two-photon transition.