Hyperfine States Research Articles

Entanglement and iSWAP gate between molecular qubits.

Quantum computation and simulation rely on long-lived qubits with controllable interactions. Trapped polar molecules have been proposed as a promising quantum computing platform, offering scalability and single-particle addressability while still leveraging inherent complexity and strong couplings of molecules1-5. Recent progress in the single quantum state preparation and coherence of the hyperfine-rotational states of individually trapped molecules allows them to serve as promising qubits6-11, with intermolecular dipolar interactions creating entanglement12,13. However, universal two-qubit gates have not been demonstrated with molecules. Here we harness intrinsic molecular resources to implement a two-qubit iSWAP gate using individually trapped X1Σ+ NaCs molecules. By allowing the molecules to interact for 664 μs at a distance of 1.9 μm, we create a maximally entangled Bell state with a fidelity of 94(3)% in trials in which both molecules are present. Using motion-rotation coupling, we measure residual excitation of the lowest few motional states along the axial trapping direction and find them to be the primary source of decoherence. Finally, we identify two non-interacting hyperfine states within the ground rotational level in which we encode a qubit. The interaction is toggled by transferring between interacting and non-interacting states to realize an iSWAP gate. We verify the gate performance by measuring its logical truth table.

Effect of dephasing on modulation transfer in potassium

In this work, experimental studies on the effect of dephasing on modulation transfer are reported. Here Potassium D1 transition, i.e., 39K 4S1/2(F) → 4P1/2(F/), is used as the medium. The 4 S→4P connection is modified by introducing two independent lasers. The separation between ground hyperfine states 4S1/2(F = 2,1) is almost half of Doppler width (~ 815 MHz). Hence, the two-level connections satisfied by respective lasers are overlapping in nature. In such cases, the existing optical pumping for particular F = 1, 2→ F/ channel influences each other. Further, the D1 transition itself is an open transition, i.e., it does not have any cyclic decay route. Hence, decay from each of the F/=2,1 states can also influence the population in the other F/state. Our pump-probe spectroscopy results clearly show the presence of Four Wave Mixing due to degenerate two-level and Vee (V) coupling, Electromagnetically Induced Transparency (EIT) signals due to single Lambda (Λ) and Double Λ connections. We have studied these signals as a function of dephasing, which is mainly contributed by transit time broadening for two different regimes of pump laser intensities: (i) below and (ii) above saturation intensity level of 4S1/2(F) → 4P1/2(F/) transition. The pump laser is current modulated, and phase-sensitive detection is performed on the probe transmission to study modulation transfer under different values of coherent dephasing. For this purpose, the beam size of the pump laser is varied systematically. This study provides a scope to explore the modulation transfer as a function of transit time broadening, and it may find applications in photonics technology where potassium vapor is used as a medium.

Chip-scale sub-Doppler atomic spectroscopy enabled by a metasurface integrated photonic emitter

We demonstrate chip-scale sub-Doppler spectroscopy in an integrated and fiber-coupled photonic-metasurface device. The device is a stack of three planar components: a photonic mode expanding grating emitter circuit with a monolithically integrated tilt-compensating dielectric metasurface, a microfabricated atomic vapor cell, and a mirror. The metasurface photonic circuit efficiently emits a 130 μm wide (1/e2 diameter) collimated surface-normal beam with only −6.3 dB loss and couples the reflected beam back into the waveguide and connecting fiber, requiring no alignment between the stacked components. We develop a simple model based on light propagation through the photonic device to interpret the atomic spectroscopy signals and explain spectral features covering the full Rb hyperfine state manifold. The demonstration of waveguide-to-waveguide coupling through the vapor cell paves the way for atomic ensembles to be used as components in complex photonic integrated circuits, allowing the unique properties of atomic systems to be available for future highly miniaturized optical devices and systems.

Laser cooling of a fermionic molecule

Only bosonic molecular species have been directly laser cooled to date, primarily due to an abundance of bosonic isotopes in nature and to their simpler hyperfine structure. Fermionic molecules provide new opportunities for ultracold chemistry, quantum simulation, and precision measurements. Here we report direct laser cooling of a fermionic molecular isotopologue, calcium monodeuteride (CaD). With a nuclear spin I=1, only 5 hyperfine states need to be addressed for rotational closure in optical cycling. These hyperfine states are unresolved for typical experimental linewidths. We present a method for efficiently producing alkaline-earth metal hydrides and deuterides. We demonstrate rotational closure and show magnetically assisted Sisyphus cooling in one dimension for a beam of CaD molecules. Our results indicate that the experimental complexity for laser cooling CaD is similar to that of calcium monohydride (CaH). Laser cooling of CaD is a promising first step for production of ultracold and trapped atomic deuterium. Published by the American Physical Society 2024

Electroweak Nuclear Properties from Single Molecular Ions in a Penning Trap.

We present a novel technique to probe electroweak nuclear properties by measuring parity violation (PV) in single molecular ions in a Penning trap. The trap's strong magnetic field Zeeman shifts opposite-parity rotational and hyperfine molecular states into near degeneracy. The weak interaction-induced mixing between these degenerate states can be larger than in atoms by more than 12 orders of magnitude, thereby vastly amplifying PV effects. The single molecule sensitivity would be suitable for applications to nuclei across the nuclear chart, including rare and unstable nuclei.

Cavity QED systems for steady-state sources of Wigner-negative light

We present a theoretical investigation of optical cavity quantum electrodynamics (cavity QED) systems, as described by the driven, open Jaynes–Cummings model and some of its variants, as potential sources of steady-state Wigner-negative light. We consider temporal modes in the continuous output field from the cavity and demonstrate pronounced negativity in their Wigner distributions for experimentally relevant parameter regimes. We consider models of both single and collective atomic spin systems, and find a rich structure of Wigner-distribution negativity as the spin size is varied. We also demonstrate an effective realization of all of the models considered using just a single 87Rb atom and based upon combinations of laser- and laser-plus-cavity-driven Raman transitions between magnetic sublevels in a single ground hyperfine state.

Magnetic resonance frequency shifts in quantum magnetometers based on the phenomenon of the optical orientation of atoms

Subject of study. Magnetic resonance frequency shifts caused by spin exchange collisions involving optically oriented alkali atoms in the ground state are studied. Aim of study. Spin-exchange collisions involving optically oriented pairs of alkali atoms of different types are theoretically studied to determine the shifts in the magnetic resonance line frequencies as a function of temperature for various pairs of alkali atoms under various optical orientation conditions in order to determine optimum constraints for the construction of quantum magnetometers with optical pumping using mixtures of alkali atoms. Method. Collisions between optically oriented alkali atoms are analyzed within the framework of quantum scattering theory, and data on the interaction potentials of alkali-atom dimers are used to calculate the scattering phases for collisions involving these potentials and the imaginary parts of the complex spin-exchange cross-section. The resulting cross sections as a function of energy were used to determine the magnetic resonance frequency shifts as a function of temperature. Main results. The magnetic resonance line frequency shifts for the following pairs of alkali atoms were obtained as a function of temperature: 39K−133Cs, 39K−85Rb, and 133Cs−85Rb. The shift in the magnetic resonance line involving the F=1 hyperfine state for a 39K−85Rb alkali-atom pair was found to pass through zero near temperature 480 K. Practical significance. The results obtained in this paper can be used to develop zero-spin-exchange-shift quantum electronic devices based on the optical orientation of atoms. In particular, it is possible to develop co-magnetometers based on the optical orientation of alkali atoms.

Dual-species Bose-Einstein condensates of Na23 and K41 with tunable interactions

We report the creation of dual-species Bose-Einstein condensates (BECs) of Na23 and K41. Favorable background scattering lengths enable efficient sympathetic cooling of K41 via forced evaporative cooling of Na23 in a plugged magnetic trap and an optical dipole trap. The 1/e lifetime of the thermal mixture in the stretched hyperfine state exceeds 5 s in the presence of background scattering. At the end of evaporation, we create dual BECs in the immiscible phase, with about 3×105 Na23 atoms surrounding 5×104 K41 atoms. To further enable the tuning of the interspecies interaction strength, we locate multiple Feshbach resonances at magnetic fields up to 100 G. The broadest s-wave resonance located at 73.4(3) G features a favorable width of 1.8(2) G. This work sets the stage for the creation of ultracold gases of strongly dipolar bosonic Na23K41 molecules as well as the exploration of many-body physics in bosonic Na23−K41 mixtures. Published by the American Physical Society 2024

Resolved Raman sideband cooling of a single optically trapped cesium atom.

We developed a resolved Raman sideband cooling scheme that can efficiently prepare a single optically trapped cesium (Cs) atom in its motional ground states. A two-photon Raman process between two outermost Zeeman sublevels in a single hyperfine state is applied to reduce the phonon number. Our scheme is less sensitive to the variation in the magnetic field than the commonly used scheme where the two outermost Zeeman sublevels belonging to the two separate ground hyperfine states are taken. Fast optical pumping with less spontaneous emission guarantees the efficiency of the cooling process. After cooling for 50 ms, 82% of the Cs atoms populate their three-dimensional ground states. Our scheme improves the long-term stability of Raman sideband cooling in the presence of magnetic field drift and is thus suitable for cooling other trapped atoms or ions with abundant magnetic sublevels.

The 5P3/2→6PJ(J=1/2,3/2) Electric Dipole Forbidden Transitions in Rubidium

This paper presents a general review of the results of the experimental and theoretical work carried out by our research group to study the 5P3/2→6PJ electric quadrupole transition in atomic rubidium. The experiments were carried out with room-temperature atoms in an absorption cell. A steady-state population of atoms in the 5P3/2 excited state is produced by a a narrow-bandwidth preparation laser locked to the D2 transition. A second CW laser is used to produce the forbidden transition with resolution of the 6PJ hyperfine states of both rubidium isotopes. The process is detected by recording the 420(422) nm fluorescence that occurs when the atoms in the 6PJ state decay directly into the 5S ground state. The fluorescence spectra show a strong dependence on the relative polarization directions of the preparation laser and the beam producing the forbidden transition. This dependence is directly related to a strong anisotropy in the populations of the 5P3/2 intermediate magnetic substates, and also to the electric quadrupole selection rules over magnetic quantum numbers. A calculation based on the rate equations that includes velocity and detuning dependent transition rates is adequate to reproduce these results. The forbidden transition is also shown to be an ideal probe to measure the Autler–Townes splitting generated in the preparation of the 5P3/2 state. Examples of spectra obtained with cold atoms in a magneto-optical trap (MOT) are also presented. These spectra show the expected Autler–Townes doublet structure with asymmetric line profiles that result as a consequence of the red-detuning of the trapping laser in the MOT.

Hyperfine transition induced by atomic motion above a paraffin-coated magnetic film

We measured transitions between the hyperfine levels of the electronic ground state of potassium-39 atoms (transition frequency: 460 MHz) as the atoms moved through a periodic magneto-static field produced above the magnetic-stripe domains of a magnetic film. The period length of the magnetic field was 3.8 µm. The atoms were incident to the field as an impinging beam with the most probable velocity of 550 m s−1 and experienced a peak oscillating field of 20 mT. Unwanted spin relaxation caused by the collisions of the atoms with the film surface was suppressed by the paraffin coating on the film. We observed increasing hyperfine transition probabilities as the frequency of the field oscillations experienced by the atoms increased from 0 to 140 MHz for the atomic velocity of 550 m s−1, by changing the incident angle of the atomic beam with respect to the stripe domains. Numerical calculation of the time evolution of the hyperfine states revealed that the oscillating magnetic field experienced by the atoms induced the hyperfine transitions, and the main process was not a single-quantum transition but rather multi-quanta transitions.

Hyperfine states of erbium doped yttrium orthosilicate for long-coherence-time quantum memories

Due to their unique optical transition at 1.5 μm, erbium-doped crystals are one of the best candidates for the realization of quantum memories at telecommunication wavelengths. While the hyperfine states of erbium doped yttrium orthosilicate hold the possibility of achieving ultra-long coherence times for a quantum memory, the complexity of their hyperfine structures leads to inaccurate theoretical prediction, thus hindering the extending of the coherence times. Here, we report a set of spin-Hamiltonian parameters with sufficient predictive power on the coherence times of the erbium hyperfine states. Our calculation simultaneously takes into account both the data measured in Electron-Paramagnetic-Resonance and Raman-heterodyne experiments. Based on the new parameters, the coherence properties of the hyperfine ground states are discussed. At zero applied magnetic field, all hyperfine transitions between the ground states are transitions with zero-first-order-Zeeman (ZEFOZ) effect, manifesting both long coherence times and strong transition strengths. By turning up the magnetic field, it is possible to further extend the coherence times to the scale of hours. The long coherence times at ZEFOZ transitions can be an important step forward in creating long-lived telecommunication quantum memories.

Dynamical mean-field-driven spinor-condensate physics beyond the single-mode approximation

$^{23}\mathrm{Na}$ spin-1 Bose-Einstein condensates are used to experimentally demonstrate that mean-field physics beyond the single-mode approximation can be relevant during the nonequilibrium dynamics. The experimentally observed spin oscillation dynamics and associated dynamical spatial structure formation confirm theoretical predictions that are derived by solving a set of coupled mean-field Gross-Pitaevskii equations [J. Jie et al., Phys. Rev. A 102, 023324 (2020)]. The experiments rely on microwave dressing of the $f=1$ hyperfine states, where $f$ denotes the total angular momentum of the $^{23}\mathrm{Na}$ atom. The fact that physics beyond the single-mode approximation at the mean-field level, i.e., spatial mean-field dynamics that distinguishes the spatial density profiles associated with different Zeeman levels, can, in certain parameter regimes, have a pronounced effect on the dynamics when the spin healing length is comparable to or larger than the size of the Bose-Einstein condensate has implications for using Bose-Einstein condensates as models for quantum phase transitions and spin squeezing studies as well as for nonlinear SU(1,1) interferometers.

Ultracold Gas of Dipolar NaCs Ground State Molecules.

We report on the creation of bosonic NaCs molecules in their absolute rovibrational ground state via stimulated Raman adiabatic passage. We create ultracold gases with up to 22 000 dipolar NaCs molecules at a temperature of 300(50)nK and a peak density of 1.0(4)×10^{12} cm^{-3}. We demonstrate comprehensive quantum state control by preparing the molecules in a specific electronic, vibrational, rotational, and hyperfine state. We measure the ground state ac polarizability at 1064nm along with the two-body loss rate, which we find to be universal. Employing the tunability and strength of the permanent electric dipole moment of NaCs, we induce dipole moments of up to 2.6D at a dc electric field of 2.1(2) kV/cm and demonstrate strong microwave coupling between the two lowest rotational states with a Rabi frequency of 2π×45 MHz. A large electric dipole moment, accessible at relatively small electric fields, makes ultracold gases of NaCs molecules well suited for the exploration of strongly interacting phases of dipolar quantum matter.

Muon capture on deuteron using local chiral potentials

The muon capture reaction μ− + d → n + n + νμ in the doublet hyperfine state is studied using nuclear potentials and consistent currents derived in the chiral effective field theory, which are local and expressed in coordinate space (the so-called Norfolk models). Only the largest contribution due to the 1S0nn scattering state is considered. Particular attention is given to the estimate of theoretical uncertainty, for which four sources have been identified: 1) the model dependence, 2) the chiral-order convergence for the weak nuclear current, 3) the uncertainty in the single-nucleon axial form factor, and 4) the numerical technique adopted to solve the bound and scattering A = 2 systems. This last source of uncertainty has turned out to be essentially negligible. For the 1S0 doublet muon capture rate ΓD(S01), we obtain ΓD(S01)=255.8(0.6)(4.4)(2.9) s−1, where the three errors come from the first three sources of uncertainty. The value for ΓD(S01) obtained within this local chiral framework is compared with previous calculations and found in very good agreement.

Optical pumping effects on high-contrast Rydberg electromagnetically induced transparency

We discuss the interplay between high-contrast Rydberg-state electromagnetically induced transparency (EIT) and optical pumping (OP) in a thermal 87Rb medium. By pumping the population to one single hyperfine state, we can enhance the interaction strength and, in principle, amplify the EIT peak. According to the measurements, the EIT peak height can be improved by a factor of two or reduced by one order of magnitude, and linewidth was slightly narrowed by the pumping effect. The EIT feature is predicted quantitatively using a Doppler-free non-perturbation numerical calculation. In both simulations and measurements, Rydberg-EIT enhancement through OP is dependent on the intensity of the probe field and the optical density. Our work clarifies the underlying mechanisms of optical pumping, making relevant studies useful in developing Rydberg-based electrometry.

Quantum degenerate Bose-Fermi atomic gas mixture of 23Na and 40K

We report a compact experimental setup for producing a quantum degenerate mixture of Bose 23Na and Fermi 40K gases. The atoms are collected in dual dark magneto–optical traps (MOT) with species timesharing loading to reduce the light-induced loss, and then further cooled using the gray molasses technique on the D 2 line for 23Na and D 1 line for 40K. The microwave evaporation cooling is used to cool 23Na in | F = 2,mF = 2〉 in an optically plugged magnetic trap, meanwhile, 40K in | F = 9/2,mF = 9/2〉 is sympathetically cooled. Then the mixture is loaded into a large volume optical dipole trap where 23Na atoms are immediately transferred to |1,1〉 for further effective cooling to avoid the strong three-body loss between 23Na atoms in |2,2〉 and 40K atoms in |9/2,9/2〉. At the end of the evaporation in optical trap, a degenerate Fermi gas of 40K with 1.9 × 105 atoms at T/TF = 0.5 in the |9/2,9/2〉 hyperfine state coexists with a Bose–Einstein condensate (BEC) of 23Na with 8 × 104 atoms in the |1,1〉 hyperfine state at 300 nK. We also can produce the two species mixture with the tunable population imbalance by adjusting the 23Na magneto–optical trap loading time.

Atom Interferometer Driven by a Picosecond Frequency Comb.

We demonstrate a light-pulse atom interferometer based on the diffraction of free-falling atoms by a picosecond frequency-comb laser. More specifically, we coherently split and recombine wave packets of cold ^{87}Rb atoms by driving stimulated Raman transitions between the |5s ^{2}S_{1/2},F=1⟩ and |5s ^{2}S_{1/2},F=2⟩ hyperfine states, using two trains of picosecond pulses in a counterpropagating geometry. We study the impact of the pulses' length as well as the interrogation time onto the contrast of the atom interferometer. Our experimental data are well reproduced by a numerical simulation based on an effective coupling that depends on the overlap between the pulses and the atomic cloud. These results pave the way for extending light-pulse interferometry to transitions in other spectral regions and therefore to other species, for new possibilities in metrology, sensing of gravito-inertial effects, and tests of fundamental physics.

Quantum Computation in a Hybrid Array of Molecules and Rydberg Atoms

We show that an array of polar molecules interacting with Rydberg atoms is a promising hybrid system for scalable quantum computation. Quantum information is stored in long-lived hyperfine or rotational states of molecules, which interact indirectly through resonant dipole-dipole interactions with Rydberg atoms. A two-qubit gate based on this interaction has a duration of 1μs and an achievable fidelity of 99.9%. The gate has little sensitivity to the motional states of the particles—the molecules can be in thermal states, the atoms do not need to be trapped during Rydberg excitation, the gate does not heat the molecules, and heating of the atoms has a negligible effect. Within a large, static array, the gate can be applied to arbitrary pairs of molecules separated by tens of micrometres, making the scheme highly scalable. The molecule-atom interaction can also be used for rapid qubit initialization and efficient, nondestructive qubit readout, without driving any molecular transitions. Single-qubit gates are driven using microwave pulses alone, exploiting the strong electric dipole transitions between rotational states. Thus, all operations required for large-scale quantum computation can be done without moving the molecules or exciting them out of their ground electronic states.Received 6 April 2022Accepted 12 August 2022DOI:https://doi.org/10.1103/PRXQuantum.3.030340Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasCold and ultracold moleculesQuantum gatesQuantum information architectures & platformsPhysical SystemsRydberg atoms & moleculesQuantum InformationAtomic, Molecular & Optical

Simultaneous sub-Doppler laser cooling of Li6 and Li7 isotopes

We report on the simultaneous sub-Doppler laser cooling of $^{6}\mathrm{Li}$ and $^{7}\mathrm{Li}$ isotopes using gray molasses operating on their respective ${D}_{1}$ atomic transitions. For $^{7}\mathrm{Li}$ we show that the sub-Doppler cooling can be achieved with two distinct $\mathrm{\ensuremath{\Lambda}}$-type transitions, where the upper level can be either of the two ${2}^{2}\phantom{\rule{0.16em}{0ex}}{P}_{1/2}$ hyperfine states. We obtain temperatures of $\ensuremath{\sim}85\phantom{\rule{0.16em}{0ex}}\ensuremath{\mu}\mathrm{K}$, with atom numbers of $\ensuremath{\sim}{10}^{8}$, and phase-space densities in the range of ${10}^{\ensuremath{-}6}\ensuremath{-}{10}^{\ensuremath{-}5}$ for both isotopes. These conditions provide a good starting point for loading the mixture into an optical dipole trap and performing evaporative cooling to quantum degeneracy. Our work provides a valuable simplification for the preparation of ultracold $^{6}\mathrm{Li}\ensuremath{-}^{7}\mathrm{Li}$ mixtures, which were proven to be a successful system for the study of impurity physics and Bose-Fermi superfluids.