Decoherence of a Single-Ion Qubit Immersed in a Spin-Polarized Atomic Bath

We report on the immersion of a spin qubit encoded in a single trapped ion into a spin-polarized neutral atom environment, which possesses both continuous (motional) and discrete (spin) degrees of freedom. The environment offers the possibility of a precise microscopic description, which allows us to understand dynamics and decoherence from first principles. We observe the spin dynamics of the qubit and measure the decoherence times ($T_1$ and $T_2$), which are determined by the spin-exchange interaction as well as by an unexpectedly strong spin-nonconserving coupling mechanism.

Figure 1

(a) Illustration of the trapped single ion spin coupled to a spin-polarized neutral atom cloud. (b) Level structure of the ${\mathrm{Yb}}^{+}$ electronic ground state in a weak magnetic field. To implement the spin-$1/2$ system, we use either the Zeeman qubit $|m_J=\pm 1/2⟩$ in the isotope ${}^{174}\mathrm{Yb}^{+}$ or the magnetic field insensitive hyperfine qubit $|F=0,m_F=0⟩$ and $|1,0⟩$ in the isotope ${}^{171}\mathrm{Yb}^{+}$. (c) The cloud of neutral ${}^{87}\mathrm{Rb}$ atoms is prepared in one of the four atomic spin states $|F=2,m_F=2{⟩}_a$,$|2,-2{⟩}_a$,$|1,1{⟩}_a$ or $|1,-1{⟩}_a$.

Figure 2

Spin-relaxation in the ${}^{174}\mathrm{Yb}^{+}$ Zeeman qubit. The probability $p_{\mathrm{Bright}}$ of the ion to occupy the bright $|\uparrow ⟩$ state after preparation in $|\uparrow ⟩$ (full symbols) or $|\downarrow ⟩$ (open symbols) in a bath of (a) $|1,1{⟩}_a$ or (b) $|2,2{⟩}_a$ atoms. Error bars denote 1 standard deviation uncertainty intervals resulting from approximately 3000 measurements per spin state. (c) The equilibrium spin states (corrected for detection efficiencies) for all four atomic bath configurations $|2,-2{⟩}_a$, $|1,-1{⟩}_a$, $|1,1{⟩}_a$, and $|2,2{⟩}_a$.

Figure 3

Hyperfine spin relaxation in ${}^{171}\mathrm{Yb}^{+}$. (a) The probability $p_{\mathrm{Bright}}$ after preparation in the $|1,0⟩$ (full symbols) or the $|0,0⟩$ (open symbols) state vs the interaction time for atoms in the $|1,-1{⟩}_a$ state. Error bars denote 1 standard deviation uncertainty intervals resulting from a total of 5000 measurements. The fit values at $t=0$ are limited by detection errors. (b) Similar data for collisions with ${}^{87}\mathrm{Rb}$ atoms in the $|2,2{⟩}_a$ state and a total of 19 000 measurements. (c)–(e) Zeeman-resolved detection within the $F=1$ manifold after preparation in $|1,0⟩$ (atoms in $|2,2{⟩}_a$) with 1200 measurements per Zeeman state. The measurements are performed by applying resonant $\pi$ pulses, exchanging the population of the dark state $|0,0⟩$ with $|1,-1⟩$, $|1,0⟩$ or $|1,1⟩$ immediately before the detection of the probability of the ion being in the dark state $p_{\mathrm{Dark}}$.

Figure 4

Spin coherence of the hyperfine clock transition $|0,0⟩\leftrightarrow |1,0⟩$ in ${}^{171}\mathrm{Yb}^{+}$. (a)–(d) Ramsey fringes recorded for increasing atomic density. (e) Ramsey contrast as a function of $t/t_L$ displays an exponential decay with a time constant of $T_2=(1.4\pm 0.2)t_L$. (f) No frequency shift of the clock transition is observed within the experimental errors. Error bars denote 1 standard deviation uncertainty intervals.