Tensor Light Shifts Research Articles

Robust storage qubits in ultracold polar molecules

Quantum states with long-lived coherence are essential for quantum computation, simulation and metrology. The nuclear spin states of ultracold molecules prepared in the singlet rovibrational ground state are an excellent candidate for encoding and storing quantum information. However, it is important to understand all sources of decoherence for these qubits, and then eliminate them, in order to reach the longest possible coherence times. Here, we fully characterise the dominant mechanisms for decoherence of a storage qubit in an optically trapped ultracold gas of RbCs molecules using high-resolution Ramsey spectroscopy. Guided by a detailed understanding of the hyperfine structure of the molecule, we tune the magnetic field to where a pair of hyperfine states have the same magnetic moment. These states form a qubit, which is insensitive to variations in magnetic field. Our experiments reveal an unexpected differential tensor light shift between the states, caused by weak mixing of rotational states. We demonstrate how this light shift can be eliminated by setting the angle between the linearly polarised trap light and the applied magnetic field to a magic angle of $\arccos{(1/\sqrt{3})}\approx55^{\circ}$. This leads to a coherence time exceeding 6.9 s (90% confidence level). Our results unlock the potential of ultracold molecules as a platform for quantum computation.

Squeezing the angular momentum of an ensemble of complex multilevel atoms

Squeezing of collective atomic spins has been shown to improve the sensitivity of atomic clocks and magnetometers to levels significantly below the standard quantum limit. In most cases the requisite atom-atom entanglement has been generated by dispersive interaction with a quantized probe field or by state-dependent collisions in a quantum gas. Such experiments typically use complex multilevel atoms like Rb or Cs, with the relevant interactions designed so that atoms behave like pseudospin-$\frac{1}{2}$ particles. We demonstrate the viability of spin squeezing for collective spins composed of the physical angular momenta of ${10}^{6}$ Cs atoms, each in an internal spin-4 hyperfine state. A peak metrological squeezing of at least 5dB is generated by quantum backaction from a dispersive quantum nondemolition (QND) measurement, implemented using a two-color optical probe that minimizes tensor light shifts without sacrificing measurement strength. Other significant developments include the successful application of composite pulse techniques for accurate dynamical control of the collective spin, enabled by broadband suppression of background magnetic fields inside a state-of-the-art magnetic shield. The absence of classical noise allows us to compare the observed quantum projection noise and squeezing to a theoretical model that properly accounts for both the relevant atomic physics and the spatial mode of the collective spin, finding good quantitative agreement and thereby validating its use in other contexts. Our work sets the stage for experiments on quantum feedback, deterministic squeezing, and closed-loop magnetometry. The implementation of real-time feedback may also create an opportunity for new types of quantum simulation, wherein the evolution of a quantum system is conditioned on the outcome of a time-continuous QND measurement. Such a scheme has the potential to access new regimes near the quantum-classical boundary, with opportunities to study long-standing issues related to quantum-classical correspondence in chaotic systems.

Enhancing Dipolar Interactions between Molecules Using State-Dependent Optical Tweezer Traps.

We show how state-dependent optical potentials can be used to trap a pair of molecules in different internal states at a separation much smaller than the wavelength of the trapping light. This close spacing greatly enhances the dipole-dipole interaction and we show how it can be used to implement two-qubit gates between molecules that are 100 times faster than existing protocols and than rotational coherence times already demonstrated. We analyze complications due to hyperfine structure, tensor light shifts, photon scattering, and collisional loss, and conclude that none is a barrier to implementing the scheme.

Second-order effects in parametric-resonance magnetometers based on atomic alignment

Optically-pumped magnetometers (OPM) based on parametric resonance allow real-time tri-axial measurement of very small magnetic fields with a single optical access to the gas cell. Most of these magnetometers rely on circularly polarized pumping light. We focus here on the ones relying on linearly polarized light, yielding atomic alignment. For these magnetometers we investigate three second order effects which appear in the usual regimes of operation, so to clarify if they translate to metrological problems like systematic errors or increased noise. The first of these effects is the breakdown of the three-step approach when the optical beam has a large intensity. The second one is the breakdown of the rotating wave approximation when the frequencies of the RF fields are not much larger than the rates of other atomic processes. The third one is the tensor light-shift which appears when the light is slightly detuned from resonance. This work should help to clarify the accuracy reachable with OPM, which is an important question notably for medical imaging applications.

The effect of tensor light shift on residual magnetic field compensation in a nuclear spin co-magnetometer

In a nuclear spin co-magnetometer, it was found that the probe light parameters have a significant impact on the transverse residual magnetic field compensation. In this paper, we demonstrated that this effect is caused by the tensor light shifts of the linearly polarized probe light. This effect can be suppressed at a certain probe light polarization. We obtained this probe light polarization experimentally and reduced the impact of probe power on magnetic field compensation by 35 times. The impact of probe light frequency is also suppressed. Furthermore, the influence of the pump power, the static magnetic field, and the cell temperature on this optimized polarization was investigated. The tensor light shift can be suppressed at about 17° polarization under different conditions in our system. Moreover, the actual residual magnetic field in the magnetic shields can be obtained, which is useful for the magnetic field design of the co-magnetometer, and this method can also be extended to other atomic devices to suppress the tensor light shift.

Measurement of the polarization‐ and orientation‐dependent scalar, vector, and tensor light shifts in 87Rb using the near‐resonant, stimulated Raman spectroscopy

AbstractWe present the polarization‐ and orientation‐dependent characteristics of the differential light shifts (DLSs) in 87Rb using the near‐resonant, stimulated Raman spectroscopy with an atomic fountain clock. Simulation and experimental results demonstrate that the Raman resonant frequencies would shift sinusoidally as the rotation of the laser's polarization vector due to the polarization‐dependent vector and tensor DLSs, and the total DLS is counteracted in some elliptically polarized laser configurations. What is more, this paper provides an alternative method to measure the effective magnetic field vector and the absolute scalar, vector, and tensor (SVT) DLSs and to verify the theoretically calculated SVT dynamical polarizabilities. These results will facilitate the evaluation and elimination of the light shift‐related systemic errors in the atomic optics‐based quantum sensors, including the atomic magnetometer, atomic interferometer, atomic clock, and quantum register.

Transmission spectroscopy of a single atom in the presence of tensor light shifts

We investigate the interplay between Zeeman and light shifts in the transmission spectrum of an optically trapped, spin-polarized Rubidium atom. The spectral shape of the transmission changes from multiple, broad resonances to a single, narrow Lorentzian with a high resonant extinction value when we increase the magnetic field strength and lower the depth of the dipole trap. We present an experimental configuration well-suited for quantum information applications that enables not only efficient light-atom coupling, but also a long coherence time between ground state hyperfine levels.

Observation of vector and tensor light shifts in Rb87 using near-resonant, stimulated Raman spectroscopy

We present the derivation of the frequency dependent scalar, vector, and tensor dynamical polarizabilities for the two hyperfine levels of the 87Rb atom 5s ground state. Based on the characterization of the dynamical polarizabilities, we analyze and measure the differential vector and tensor light shift between the 5s ground state sub-levels with near-resonant, stimulated Raman transitions. These results clarify that the tensor polarizabilities for the ground states of alkali atoms are absent when the light field is far-detuned from the atomic resonance and the total electronic angular momentum J is a good quantum number. In the near resonant case, the light shifts are non-trivial and the determination of the frequency dependent vector and tensor dynamic polarizabilities will help to achieve higher fidelities for applications of neutral atoms in quantum information and precision measurements.

Mapping the absolute magnetic field and evaluating the quadratic Zeeman-effect-induced systematic error in an atom interferometer gravimeter

Precisely evaluating the systematic error induced by the quadratic Zeeman effect is important for developing atom interferometer gravimeters aiming at an accuracy in the regime ( ). This paper reports on the experimental investigation of Raman spectroscopy-based magnetic field measurements and the evaluation of the systematic error in the Gravimetric Atom Interferometer (GAIN) due to quadratic Zeeman effect. We discuss Raman duration and frequency step size dependent magnetic field measurement uncertainty, present vector light shift (VLS) and tensor light shift (TLS) induced magnetic field measurement offset, and map the absolute magnetic field inside the interferometer chamber of GAIN with an uncertainty of 0.72 nT and a spatial resolution of 12.8 mm. We evaluate the quadratic Zeeman effect induced gravity measurement error in GAIN as . The methods shown in this paper are important for precisely mapping the absolute magnetic field in vacuum and reducing the quadratic Zeeman effect induced systematic error in Raman transition-based precision measurements, such as atomic interferometer gravimeters.

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.

Using tensor light shifts to measure and cancel a cell's quadrupolar frequency shift

We have developed a technique that uses the tensor light shift to measure and cancel the frequency shift produced by the quadrupolar anisotropy of a vapor cell. We demonstrate the technique on the $6{S}_{1/2},\phantom{\rule{0.16em}{0ex}}F=4$ level of Cs using the ${D}_{1}$ transition. The method extends our ability to study quadrupolar wall interactions beyond diamagnetic atoms. We have deduced the twist angle per wall adhesion for cesium on an alkene coating to be ${\ensuremath{\theta}}_{\mathrm{Cs}\ensuremath{-}\mathrm{alkene}}=1.4\phantom{\rule{4pt}{0ex}}\mathrm{mrad}$. This value is about 37 times larger than the twist angle observed in $^{131}\text{Xe}$, suggesting that it is not produced by the interaction of the nuclear quadrupole moment with a collisional electric-field gradient. Alternative mechanisms that may be responsible for the observed quadrupolar frequency shifts are discussed. By canceling the cell-induced quadrupole shift we have extended our cells' effective spin-relaxation times by as much as a factor of 2. This cancellation improves magnetometer sensitivity in highly anisotropic cells and could reduce systematic uncertainties in some precision measurements.

Inhomogeneous broadening of optical transitions of 87Rb atoms in an optical nanofiber trap

We experimentally demonstrate optical trapping of atoms using a two-color evanescent field around an optical nanofiber. In our trapping geometry, a blue-detuned traveling wave whose polarization is nearly parallel to the polarization of a red-detuned standing wave produces significant vector light shifts that lead to broadening of the absorption profile of a near-resonant beam at the trapping site. A model that includes scalar, vector, and tensor light shifts of the probe transition - from the trapping beams, weighted by the temperature-dependent position of the atoms in the trap, qualitatively describes the observed asymmetric profile and explains differences with previous experiments that used Cs atoms. The model provides a consistent way to extract the number of atoms in the trap.

Competition between the tensor light shift and nonlinear Zeeman effect

Many precision measurements (e.g., in spectroscopy, atomic clocks, quantum-information processing, etc.) suffer from systematic errors introduced by the light shift. In our experimental configuration, however, the tensor light shift plays a positive role enabling the observation of spectral features otherwise masked by the cancellation of the transition amplitudes and creating resonances at a frequency unperturbed either by laser power or beam inhomogeneity. These phenomena occur thanks to the special relation between the nonlinear Zeeman and light shift effects. The interplay between these two perturbations is systematically studied and the cancellation of the nonlinear Zeeman effect by the tensor light shift is demonstrated.

Quantum Control of the Hyperfine Spin of a Cs Atom Ensemble

We demonstrate quantum control of a large spin angular momentum associated with the F=3 hyperfine ground state of 133Cs. Time-dependent magnetic fields and a static tensor light shift are used to implement near-optimal controls and map a fiducial state to a broad range of target states, with yields in the range 0.8-0.9. Squeezed states are produced also by an adiabatic scheme that is more robust against errors. Universal control facilitates the encoding and manipulation of qubits and qudits in atomic ground states and may lead to the improvement of some precision measurements.

Nuclear spin effects in optical lattice clocks

We present a detailed experimental and theoretical study of the effect of nuclear spin on the performance of optical lattice clocks. With a state-mixing theory including spin-orbit and hyperfine interactions, we describe the origin of the $^{1}S_{0}\text{\ensuremath{-}}^{3}P_{0}$ clock transition and the differential $g$ factor between the two clock states for alkaline-earth-metal(-like) atoms, using $^{87}\mathrm{Sr}$ as an example. Clock frequency shifts due to magnetic and optical fields are discussed with an emphasis on those relating to nuclear structure. An experimental determination of the differential $g$ factor in $^{87}\mathrm{Sr}$ is performed and is in good agreement with theory. The magnitude of the tensor light shift on the clock states is also explored experimentally. State specific measurements with controlled nuclear spin polarization are discussed as a method to reduce the nuclear spin-related systematic effects to below ${10}^{\ensuremath{-}17}$ in lattice clocks.

Measurement of an electron’s electric dipole moment using Cs atoms trapped in optical lattices

We propose to measure the electron's permanent electric dipole moment (EDM) using cesium atoms trapped in a sparsely populated, trichromatic, far blue-detuned three-dimensional (3D) optical lattice. In the proposed configuration, the atoms can be strongly localized near the nodes of the light field and isolated from each other, leading to a strong suppression of the detrimental effects of atom-atom and atom-field interactions. Three linearly polarized standing waves with different frequencies create an effectively linearly polarized 3D optical lattice and lead to a strong reduction of the tensor light shift, which remains a potential source of systematic error. Other systematics concerning external field instability and gradients and higher-order polarizabilities are discussed. Furthermore, auxiliary atoms can be loaded into the same lattices as effective ``comagnetometers'' to monitor various systematic effects, including magnetic-field fluctuations and imperfect electric-field reversal. We estimate that a sensitivity 100 times higher than the current upper bound for the electron's EDM of $4\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}27}e\mathrm{cm}$ can be achieved with the proposed technique.

Zeeman frequency shifts in an optical dipole trap used to search for an electric-dipole moment

We calculate the Zeeman frequency shifts due to interactions with the light in a far-off-resonance optical dipole trap. These shifts are important for potential use of such a trap to search for an atomic permanent electric-dipole moment ~EDM!. We present numerical results for Cs and Hg, as examples of paramagnetic and diamagnetic atoms. The vector and tensor light shifts are calculated for a large range of trap optical frequencies, for both red-detuned and blue-detuned traps. We also consider frequency shifts resulting from magnetic dipole and electric quadrupole transitions mixed in by a static electric field. These shifts are particularly important for EDM experiments since they are linear in the electric field. The Zeeman frequency shifts represent a substantial problem for EDM experiments in a dipole trap and must be controlled with care to achieve theoretical sensitivity. @S1050-2947~99!02806-1# PACS number~s!: 32.80.Pj, 32.60.1i, 32.10.Dk, 11.30.Er I. INTRODUCTION The search for a permanent electric-dipole moment ~EDM! is an effective method of probing for physics beyond the standard model @1#. A nonzero value of the EDM requires violation of T and P invariance. If the CPT symmetry is not violated, it also implies CP violation. Within the standard model the EDMs are unmeasurably small, but many extensions of the standard model predict EDMs well within experimental reach. Techniques of laser cooling and trapping of neutral atoms open new possibilities for EDM experiments @2,3#. In one of the more promising methods, cold atoms are held between high-voltage electrodes in an optical dipole trap, and the coupling between the static electric field and the atomic EDM produces a shift of the Zeeman levels of the atoms. However, the Zeeman levels would also be shifted by the interactions with the trapping laser fields. In this paper we present a systematic analysis of the various Zeeman energy shifts due to the laser fields in an optical dipole trap, and discuss how they might limit the sensitivity of an EDM experiment. We find that such shifts will impose tight constraints on the design of the experiment. An atom with a permanent electric-dipole moment d and a magnetic dipole moment m interacts with electric and magnetic fields E and B according to the following Hamiltonian,