Hyperfine States Research Articles

Linear and nonlinear crystal optics using the magnetic field of light

We study the $^{7}F_{0}\ensuremath{\rightarrow}^{5}D_{1}$ magnetic-dipole transition in the $4f$ shell of europium ions at a wavelength of 527.5 nm and demonstrate spectral hole burning, ion class selection, and optical pumping to specific ground hyperfine states. We then use the narrow lines of the selected ions to observe linear group delay of a weak probe pulse with a group velocity of $c/3800$. We also demonstrate electromagnetically induced transparency by establishing a $\mathrm{\ensuremath{\Lambda}}$ scheme between the ground hyperfine levels and driving the ions to a dark state.

One-dimensional localized modes of spin-orbit-coupled Bose-Einstein condensates with spatially periodic modulated atom-atom interactions: Nonlinear lattices

Bose-Einstein condensates (BECs) provide a clear and controllable platform to study diverse intriguing emergent nonlinear effects that appear too in other physical settings, such as bright and dark solitons in mean-field theory as well as many-body physics. Various ways have been elaborated to stabilize bright solitons in BECs, three promising schemes among which are: optical lattices formed by counterpropagating laser beams, nonlinear managements mediated by Feshbach resonance, spin-orbit coupling engineered by dressing atomic spin states (hyperfine states of spinor atomic BECs) with laser beams. By combing the latter two schemes, we discover, from theory to calculations, that the two-component BECs with a spin-orbit coupling and cubic atom-atom interactions, whose nonlinear distributions exhibit a well-defined spatially periodic modulation (nonlinear lattice), can support one-dimensional localized modes of two kinds: fundamental solitons (with a single peak), and soliton pairs comprised of dipole solitons (anti-phase) or two-peak solitons (in-phase). The influence of three physical parameters: chemical potential of the system, strengths of both the Rashba spin-orbit coupling and atom-atom interactions, on the existence and stability of the localized modes is investigated based on linear-stability analysis and direct perturbed simulations. In particular, we demonstrate that the localized modes can be stable objects provided always that both the inter- and intraspecies interactions are attractive.

Optical Spin-Wave Storage in a Solid-State Hybridized Electron-Nuclear Spin Ensemble.

Solid-state impurity spins with optical control are currently investigated for quantum networks and repeaters. Among these, rare-earth-ion doped crystals are promising as quantum memories for light, with potentially long storage time, high multimode capacity, and high bandwidth. However, with spins there is often a tradeoff between bandwidth, which favors electronic spin, and memory time, which favors nuclear spins. Here, we present optical storage experiments using highly hybridized electron-nuclear hyperfine states in ^{171}Yb^{3+}:Y_{2}SiO_{5}, where the hybridization can potentially offer both long storage time and high bandwidth. We reach a storage time of 1.2ms and an optical storage bandwidth of 10MHz that is currently only limited by the Rabi frequency of the optical control pulses. The memory efficiency in this proof-of-principle demonstration was about 3%. The experiment constitutes the first optical storage using spin states in any rare-earth ion with electronic spin. These results pave the way for rare-earth based quantum memories with high bandwidth, long storage time, and high multimode capacity, a key resource for quantum repeaters.

Magnetic tuning of ultracold barrierless chemical reactions

While attaining external field control of bimolecular chemical reactions has long been a coveted goal of physics and chemistry, the role of hyperfine interactions and dc magnetic fields in achieving such control has remained elusive. We develop an extended coupled-channel statistical theory of barrierless atom-diatom chemical reactions, and apply it to elucidate the effects of magnetic fields and hyperfine interactions on the ultracold chemical reaction Li($^2\text{S}_{1/2}$) + CaH($^2\Sigma^+$) $\to$ LiH($^1\Sigma^+$) + Ca($^1\text{S}_{0}$) on a newly developed set of ab initio potential energy surfaces. We observe large field effects on the reaction cross sections, opening up the possibility of controlling ultracold barrierless chemical reactions by tuning selected hyperfine states of the reactants with an external magnetic field.

Cross-dimensional relaxation of Li7−Rb87 atomic gas mixtures in a spherical-quadrupole magnetic trap

We measure the interspecies interaction strength between $^7$Li and $^{87}$Rb atoms through cross-dimensional relaxation of two-element gas mixtures trapped in a spherical quadrupole magnetic trap. We record the relaxation of an initial momentum-space anisotropy in a lithium gas when co-trapped with rubidium atoms, with both species in the $|F=1, m_F = -1\rangle$ hyperfine state. Our measurements are calibrated by observing cross-dimensional relaxation of a $^{87}$Rb-only trapped gas. Through Monte Carlo simulations, we compare the observed relaxation to that expected given the theoretically predicted energy-dependent differential cross section for $^7$Li-$^{87}$Rb collisions. The experimentally observed relaxation occurs significantly faster than predicted theoretically, a deviation that appears incompatible with other experimental data characterising the $^7$Li-$^{87}$Rb molecular potential.

Protocol for optically pumping AlH+ to a pure quantum state.

We propose an optical pumping scheme to prepare trapped AlH+ molecules in a pure state, the stretched hyperfine state of the rovibronic ground manifold |X2Σ+, v = 0, N = 0 . Our scheme utilizes linearly-polarized and circularly-polarized fields of a broadband pulsed laser to cool the rotational degree of freedom and drive the population to the hyperfine state, respectively. We simulate the population dynamics by solving a representative system of rate equations that accounts for the laser fields, blackbody radiation, and spontaneous emission. In order to model the hyperfine structure, new hyperfine constants of the A2Π excited state were computed using a RASSCF wavefunction. We find that adding an infrared laser to drive the 1-0 vibrational transition within the X2Σ+ manifold accelerates the cooling process. The results show that, under optimal conditions, the population in the target state of the rovibronic ground manifold can reach 63% after 68 μs (330 ms) and 95% after 25 ms (1.2 s) with (without) the infrared laser.

Coherent manipulation of the internal state of ultracold 87Rb133Cs molecules with multiple microwave fields.

We explore coherent multi-photon processes in 87Rb133Cs molecules using 3-level lambda and ladder configurations of rotational and hyperfine states, and discuss their relevance to future applications in quantum computation and quantum simulation. In the lambda configuration, we demonstrate the driving of population between two hyperfine levels of the rotational ground state via a two-photon Raman transition. Such pairs of states may be used in the future as a quantum memory, and we measure a Ramsey coherence time for a superposition of these states of 58(9) ms. In the ladder configuration, we show that we can generate and coherently populate microwave dressed states via the observation of an Autler-Townes doublet. We demonstrate that we can control the strength of this dressing by varying the intensity of the microwave coupling field. Finally, we perform spectroscopy of the rotational states of 87Rb133Cs up to N = 6, highlighting the potential of ultracold molecules for quantum simulation in synthetic dimensions. By fitting the measured transition frequencies we determine a new value of the centrifugal distortion coefficient Dv = h × 207.3(2) Hz.

Magnetic field effects in rigidly linked D-A dyads: Extreme on-resonance quantum coherence effect on charge recombination

Charge recombination in the photoinduced charge separated (CS) state of a rigidly linked donor/bridge/acceptor triad with a triarylamine (TAA) donor, a 1,3-diethynyl-2,5-dimethoxy benzene bridge (OMe), and a perylenediimide (PDI) unit as an acceptor, represents a spin chemical paradigm case of a rigid radical ion pair formed with singlet spin and recombining almost exclusively to the locally excited PDI triplet state (3PDI). The magnetic field dependence of the CS state decay and 3PDI formation kinetics are investigated from 0 to 1800 mT by nanosecond laser flash spectroscopy. The time-resolved magnetic field affected reaction yields spectra of the CS state population and 3PDI population exhibit a sharp and deep resonance at 18.9 mT, indicating level crossing of the S and T+ levels separated by an exchange interaction of J = 18.9/2 mT at zero field. The kinetics are biexponential around the resonance field and monoexponential outside that range. The monoexponential behavior can be simulated by a classical kinetic model assuming a single field dependent double Lorentzian function for the energy gap dependence of all spin conversion processes. The full field dependence of the kinetics has been simulated quantum theoretically. It has been shown that incoherent and coherent hyperfine coupling contribute to S/T+ spin conversion at all fields and that the biexponentiality of the kinetics at resonance is due to a partitioning of the overall kinetics into 2/3 of the singlet hyperfine states exhibiting strong isotropic coupling to T+ and 1/3 of the singlet hyperfine states that do not or only weakly couple isotropically to T+.

Bi-chromatic adiabatic shells for atom interferometry

Free space atom-interferometry traditionally suffers from the large distances that atoms have to fall in order to achieve long interaction times. Trapped atom interferometry is emerging as a powerful way of achieving long interaction times in a reduced experimental volume. Here, we demonstrate bi-chromatic adiabatic magnetic shell traps as a novel tool for matterwave interferometry. We dress the magnetic hyperfine states of the F = 1 and F = 2 Rubidium 87 Bose–Einstein Condensates thus creating two independently controllable shell traps of which we use the and adiabatic states. Using microwave pulses, we put atoms originally loaded into one of the two shell-traps into a superposition between the two shell traps. Since the two traps can be manipulated independently, their position and vertical curvature can be matched, thus creating a good starting point for an atom interferometer. This interferometer can be sensitive to spatially varying electric or magnetic fields, which could be DC or RF magnetic fields or microwaves. We demonstrate that the trap-matching afforded by the independent control of the shell traps allows for a tenfold increase in coherence times when compared to adiabatic potentials created by a single RF-frequency. For large-radius shells the atoms are confined to a 2D surface enabling highly sensitive imaging matterwave interferometers.

Hyperfine-state dependence of highly efficient amplification from diode-pumped cesium vapor.

We report optical amplification with an optical-to-optical conversion efficiency of 70 ± 1% from a diode-pumped Cs vapor cell. When pump (852 nm; D2-line) and signal (895 nm; D1-line) lasers with a narrow spectral width of ∼2 MHz are resonant on the hyperfine states (F = 3 or 4) of the 6S1/2 state, we observe that the amplification factors are significantly changed according to the hyperfine-state combination of the pump and signal lasers. We find that the optical frequencies of the pumping and signal lasers need to be controlled near the hyperfine state of 6S1/2 (F = 4) to obtain an efficient diode-pumped alkali amplifier (DPAA). To realize highly efficient optical gain conditions, both the spatial modes of the pump and signal lasers are made to overlap in the Cs vapor cell with the use of a single-mode optical fiber. An amplification factor of 430 ± 15 is achieved under the following conditions: cell temperature of 90 °C, signal power of 0.1 mW, and pump power of 200 mW. We believe that our results can aid in the development of highly efficient diode-pumped alkali-vapor lasers and amplifiers.

Modular quantum computation in a trapped ion system

Modern computation relies crucially on modular architectures, breaking a complex algorithm into self-contained subroutines. A client can then call upon a remote server to implement parts of the computation independently via an application programming interface (API). Present APIs relay only classical information. Here we implement a quantum API that enables a client to estimate the absolute value of the trace of a server-provided unitary operation U. We demonstrate that the algorithm functions correctly irrespective of what unitary U the server implements or how the server specifically realizes U. Our experiment involves pioneering techniques to coherently swap qubits encoded within the motional states of a trapped {}^{171}{{rm{Yb}}}^{+}, ion, controlled on its hyperfine state. This constitutes the first demonstration of modular computation in the quantum regime, providing a step towards scalable, parallelization of quantum computation.

Spinor Bose-Einstein condensate interferometer within the undepleted pump approximation: Role of the initial state

Most interferometers operate with photons or dilute, non-condensed cold atom clouds in which collisions are strongly suppressed. Spinor Bose-Einstein condensates (BECs) provide an alternative route toward realizing three-mode interferometers; in this realization, spin-changing collisions provide a resource that generates mode entanglement. Working in the regime where the pump mode, i.e., the m=0 hyperfine state, has a much larger population than the side or probe modes (m=+1 and m=-1 hyperfine states), f=1 spinor BECs approximate SU(1,1) interferometers. We derive analytical expressions within the undepleted pump approximation for the phase sensitivity of such an SU(1,1) interferometer for two classes of initial states: pure Fock states and coherent spin states. The interferometer performance is analyzed for initial states without seeding, with single-sided seeding, and with double-sided seeding. The validity regime of the undepleted pump approximation is assessed by performing quantum calculations for the full spin Hamiltonian. Our analytical results and the associated dynamics are expected to guide experiments as well as numerical studies that explore regimes where the undepleted pump approximation makes quantitatively or qualitatively incorrect predictions.

Leakage mitigation for quantum error correction using a mixed qubit scheme

Leakage errors take qubits out of the computational subspace and will accumulate if not addressed. A leaked qubit will reduce the effectiveness of quantum error correction protocols due to the cost of implementing leakage reduction circuits and the harm caused by interacting leaked states with qubit states. Ion trap qubits driven by Raman gates have a natural choice between qubits encoded in magnetically insensitive hyperfine states that can leak and qubits encoded in magnetically sensitive Zeeman states of the electron spin that cannot leak. In our previous work, we compared these two qubits in the context of the toric code with a depolarizing leakage error model and found that for magnetic field noise with a standard deviation less than 32 $\mu$G that the $^{174}$Yb$^+$ Zeeman qubit outperforms the $^{171}$Yb$^+$ hyperfine qubit. Here we examine a physically motivated leakage error model based on ions interacting via the Molmer-Sorenson gate. We find that this greatly improves the performance of hyperfine qubits but the Zeeman qubits are more effective for magnetic field noise with a standard deviation less than 10 $\mu$G. At these low magnetic fields, we find that the best choice is a mixed qubit scheme where the hyperfine qubits are the ancilla and the leakage is handled without the need of an additional leakage reduction circuit.

Magnetic Feshbach resonances in ultracold collisions between Cs and Yb atoms

We investigate magnetically tunable Feshbach resonances in ultracold collisions between ground-state Yb and Cs atoms, using coupled-channel calculations based on an interaction potential recently determined from photoassociation spectroscopy. We predict resonance positions and widths for all stable isotopes of Yb, together with resonance decay parameters where appropriate. The resonance patterns are richer and more complicated for fermionic Yb than for spin-zero isotopes, because there are additional level splittings and couplings due to scalar and tensorial Yb hyperfine interactions. We examine collisions involving Cs atoms in a variety of hyperfine states, and identify resonances that appear most promising for experimental observation and for magnetoassociation to form ultracold CsYb molecules.

Magnetic Phase Transition in a Mixture of Two Interacting Superfluid Bose Gases at Finite Temperature.

The miscibility condition for a binary mixture of two interacting Bose-Einstein condensates is shown to be deeply affected by interaction driven thermal fluctuations. These give rise to a first order phase transition to a demixed phase with full spatial separation of the two condensates, even if the mixture is miscible at zero temperature. Explicit predictions for the isothermal compressibility, the spin susceptibility, and the phase transition temperature T_{M} are obtained in the framework of Popov theory, which properly includes beyond mean-field quantum and thermal fluctuations in both the spin and density channels. For a mixture of two sodium condensates occupying the hyperfine states |F=1⟩,|m_{F}=1⟩ and |F=1,m_{F}=-1⟩, respectively, T_{M} is predicted to occur at about 0.7 times the usual BEC critical temperature.

Decay of the relative phase domain wall into confined vortex pairs: The case of a coherently coupled bosonic mixture

A domain wall of relative phase in a flattened harmonically-trapped Bose-Einstein condensed mixture of two atomic hyperfine states, subject to a stationary Rabi coupling of intensity $\Omega$, is predicted to decay through two different mechanisms. For small values of $\Omega$ the instability has an energetic nature and is associated with the formation of a vortex-antivortex pair of the same atomic hyperfine states, whose motion inside the trap causes the emergence of magnetization, the bending of the domain wall and its consequent fragmentation. For large values of $\Omega$ the domain wall instead undergoes a dynamic snake instability, caused by the negative value of its effective mass and results in the fast fragmentation of the wall into smaller domain walls confining vortex pairs of different atomic species. Numerical predictions are given by solving the time-dependent Gross-Pitaevskii equation in experimentally available configurations of mixtures of sodium atomic gases.

Suppressing Inhomogeneous Broadening in a Lutetium Multi-ion Optical Clock.

We demonstrate precision measurement and control of inhomogeneous broadening in a multi-ion clock consisting of three ^{176}Lu^{+} ions. Microwave spectroscopy between hyperfine states in the ^{3}D_{1} level is used to characterize differential systematic shifts between ions, most notably those associated with the electric quadrupole moment. By appropriate alignment of the magnetic field, we demonstrate suppression of these effects to the ∼10^{-17} level relative to the ^{1}S_{0}↔^{3}D_{1} optical transition frequency. Correlation spectroscopy on the optical transition demonstrates the feasibility of a 10-s Ramsey interrogation in the three ion configuration with a corresponding projection noise limited stability of σ(τ)=8.2×10^{-17}/sqrt[τ].

Simultaneous Readout of Noncommuting Collective Spin Observables beyond the Standard Quantum Limit.

We augment the information extractable from a single absorption image of a spinor Bose-Einstein condensate by coupling to initially empty auxiliary hyperfine states. Performing unitary transformations in both the original and auxiliary hyperfine manifold enables the simultaneous measurement of multiple spin-1 observables. We apply this scheme to an elongated atomic cloud of ^{87}Rb to simultaneously read out three orthogonal spin directions and with that directly access the spatial spin structure. The readout even allows the extraction of quantum correlations which we demonstrate by detecting spin-nematic squeezing without state tomography.

Observation of a transition between dynamical phases in a quantum degenerate Fermi gas.

A proposed paradigm for out-of-equilibrium quantum systems is that an analog of quantum phase transitions exists between parameter regimes of qualitatively distinct time-dependent behavior. Here, we present evidence of such a transition between dynamical phases in a cold-atom quantum simulator of the collective Heisenberg model. Our simulator encodes spin in the hyperfine states of ultracold fermionic potassium. Atoms are pinned in a network of single-particle modes, whose spatial extent emulates the long-range interactions of traditional quantum magnets. We find that below a critical interaction strength, magnetization of an initially polarized fermionic gas decays quickly, while above the transition point, the magnetization becomes long-lived because of an energy gap that protects against dephasing by the inhomogeneous axial field. Our quantum simulation reveals a nonequilibrium transition predicted to exist but not yet directly observed in quenched s-wave superconductors.

Ultracold collisions of Cs atoms in excited Zeeman and hyperfine states

We investigate Cs+Cs scattering in excited Zeeman and hyperfine states. We calculate the real and imaginary parts of the s-wave scattering length; the imaginary part directly provides the rate coefficient for 2-body inelastic loss, while the real part allows us to identify regions of magnetic field where 3-body recombination will be slow. We identify field regions where Cs in its $(f,m_f)=(3,+2)$ and $(3,+1)$ states may be stable enough to allow Bose-Einstein condensation, and additional regions for these and the $(3,0)$ and $(3,-3)$ states where high-density clouds should be long-lived.