We study fundamental features of spin current in a very weakly interacting Fermi gas of $^6$Li. By creating a spin current and then reversing its flow, we demonstrate control of the spin current. This reversal is predicted by a spin vector evolution equation in energy representation, which shows how the spin and energy of individual atoms become correlated in the nearly undamped regime of the experiments. The theory provides a simple physical description of the spin current and explains both the large amplitude and the slow temporal evolution of the data. Our results have applications in studying and controlling fundamental spin interactions and spin currents in ultra-cold gases.

Controlling spin current in a trapped Fermi gas

We report the observation of coherent heteronuclear spin dynamics driven by interspecies spin-spin interaction in an ultracold spinor mixture, which manifests as periodical and well-correlated spin oscillations between two atomic species. In particular, we investigate the magnetic field dependence of the oscillations and find a resonance behavior which depends on both the linear and quadratic Zeeman effects and the spin-dependent interaction. We also demonstrate a unique knob for controlling the spin dynamics in the spinor mixture with species-dependent vector light shifts.

http://absimage.aps.org/image/DAMOP15/MWS_DAMOP15-2015-000475.pdf

Coherent heteronuclear spin dynamics in an ultracold spin-1 mixture

In the mixture of ultracold spin-1 atoms of two different species A and B (e.g., $^{23}\mathrm{Na}$ (A) and $^{87}\mathrm{Rb}$ (B)), the interspecies singlet-pairing process ${\mathrm{A}}_{+1}+{\mathrm{B}}_{\ensuremath{-}1}\ensuremath{\rightleftharpoons}{\mathrm{A}}_{\ensuremath{-}1}+{\mathrm{B}}_{+1}$ can be induced by the spin-dependent interatomic interaction, where subscript $\ifmmode\pm\else\textpm\fi{}1$ denotes the magnetic quantum number. Nevertheless, one cannot isolate this process from other spin-changing processes, which are usually much stronger, by tuning the bias real magnetic field. As a result, it is difficult to clearly observe the singlet-pairing process and precisely measure the corresponding interaction strength. In this work we propose to control the singlet-pairing process via combining the real magnetic field and a laser-induced species-dependent synthetic magnetic field. With our approach one can significantly enhance this process and simultaneously suppress all other spin-changing processes. We illustrate our approach for both a confined two-atom system and a binary mixture of spinor Bose-Einstein condensates. Our control scheme is helpful for the precise measurement of the weak singlet-pairing interaction strength and the entanglement generation of two different atoms.

Laser control of the singlet-pairing process in an ultracold spinor mixture

Coherent control steers a quantum system from an initial state to a target state by controlling quantum interference phenomena via an external field, which is central to vast applications ranging from quantum information processing to attosecond physics. Here, we analyze the quantum pathways interference in two-color coherent control of photoemission using exact analytical solutions of the time-dependent Schr\"odinger equation. The theory includes all possible quantum pathways and their interference terms. Constructive (or destructive) interferences among the pathways leads to the maximum (or minimum) emission with varying phase delay of the two-color lasers. It is found that increasing the intensity ratio of the second harmonic $(2\ensuremath{\omega})$ to fundamental $(\ensuremath{\omega})$ lasers results in less contribution from the $\ensuremath{\omega}$ pathway (absorption of $\ensuremath{\omega}$ photons only) and more contribution from multicolor pathway (simultaneous absorption of both $\ensuremath{\omega}$ and $2\ensuremath{\omega}$ photons) and $2\ensuremath{\omega}$ pathway (absorption of $2\ensuremath{\omega}$ photons only), and therefore stronger pathways interference and increased visibility larger than 95%. Increasing bias voltages shifts the dominant emission to processes with lower-order photon absorption, which sequentially decreases the interference between the $\ensuremath{\omega}$ and the $2\ensuremath{\omega}$ pathways, and between single-color and multicolor pathways, leading to two peaks in the visibility. 

Unraveling quantum pathways interference in two-color coherent control of photoemission with bias voltages

This work studies heteronuclear spinor gases and characterizes the collision channels that can transfer magnetization from one element to another, using spin relaxation from different initial states.

Collisional spin transfer in an atomic heteronuclear spinor Bose gas

Multiphoton ionization provides a clear window into the nature of electron correlations in the helium atom. In the present study, the final-state energy range extends up to the region near the $N=2$ and $N=3$ ionization thresholds, where two-photon ionization proceeds via continuum intermediate states above the lowest threshold. Our calculations are performed using multichannel quantum defect theory (MQDT) and the streamlined $R$-matrix method. The sum and integration over all intermediate states in the two-photon ionization amplitude is evaluated using the inhomogeneous $R$-matrix method developed by Robicheaux and Gao. The seamless connection of that method with MQDT allows us to present high-resolution spectra of the final-state Rydberg resonances. Our analysis classifies the resonances above the $N=2$ threshold in terms of their group theory quantum numbers. Their dominant decay channels are found to obey the previously conjectured propensity rule far more weakly for these even-parity states than was observed for the odd-parity states relevant to single-photon ionization.

Two-photon above-threshold ionization of helium

Coherent control of interfering one- and two-photon processes has for decades been the subject of research to achieve the redirection of photocurrent. The present study develops two-pathway coherent control of ground-state helium atom above-threshold photoionization for energies up to the $N=2$ threshold, based on a multichannel quantum defect and R-matrix calculation. Three parameters are controlled in our treatment: the optical interference phase $\mathrm{\ensuremath{\Delta}}\mathrm{\ensuremath{\Phi}}$, the reduced electric field strength $\ensuremath{\chi}={\mathcal{E}}_{\ensuremath{\omega}}^{2}/{\mathcal{E}}_{2\ensuremath{\omega}}$, and the final state energy $\ensuremath{\epsilon}$. A small energy change near a resonance is shown to flip the emission direction of photoelectrons with high efficiency, through an example where $90%$ of photoelectrons whose energy is near the $2{p}^{2}{\phantom{\rule{4pt}{0ex}}}^{1}{S}^{e}$ resonance flip their emission direction. However, the large fraction of photoelectrons ionized at the intermediate state energy, which are not influenced by the optical control, make this control scheme challenging to realize experimentally.

Resonant control of photoelectron directionality by interfering one- and two-photon pathways

We observe spin transfer within a non-degenerate heteronuclear spinor atomic gas comprised of a small $^7$Li population admixed with a $^{87}$Rb bath, with both elements in their $F=1$ hyperfine spin manifolds and at temperatures of 10's of $\mu$K. Prepared in a non-equilibrium initial state, the $^7$Li spin distribution evolves through incoherent spin-changing collisions toward a steady-state distribution. We identify and measure the cross-sections of all three types of spin-dependent heteronuclear collisions, namely the spin-exchange, spin-mixing, and quadrupole-exchange interactions, and find agreement with predictions of heteronuclear $^7$Li-$^{87}$Rb interactions at low energy. Moreover, we observe that the steady state of the $^7$Li spinor gas can be controlled by varying the composition of the $^{87}$Rb spin bath with which it interacts.

pdf/collisional-spin-transfer-in-an-atomic-heteronuclear-spinor-2fl2k3f0fm.pdf

Phase lag associated with coherent control where an excited system decays into more than one product channel has been subjected to numerous investigations. Although previous theoretical studies have treated the phase lag across resonances in model calculations, quantitative agreement has never been achieved between the theoretical model and experimental measurements of phase lag from the $\omega-2\omega$ ionization of atomic barium \cite{PhysRevLett.98.053001,PhysRevA.76.053401}, suggesting that a toy model with phenomenological parameters is inadequate to describe the observed phase lag behavior. Here the phase lag is treated quantitatively from a multichannel coupling formulation, and our calculations based on multichannel quantum defect and $R$-matrix treatment achieves good agreement with the experimental observations. Our treatment also develops formulas to describe the effects of hyperfine depolarization on multiphoton ionization processes, and further, identifies resonances between $Ba^{+}$ $5d_{3/2}$ and $5d_{5/2}$ thresholds that have apparently never been experimentally observed and classified.

Multichannel photoelectron phase lag across atomic barium autoionizing resonances

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Papers

Two-photon above-threshold ionization of helium

Collisional spin transfer in an atomic heteronuclear spinor Bose gas

Resonant control of photoelectron directionality by interfering one- and two-photon pathways

Collisional spin transfer in an atomic heteronuclear spinor Bose gas

Multichannel photoelectron phase lag across atomic barium autoionizing resonances