Entangling ions with engineered light gradients

Abstract

Spectral crowding of collective motional modes limits the fidelity of entangling interactions in trapped-ion quantum processors by inducing off-resonant coupling to spectator modes. We introduce a geometric-phase entangling interaction driven by a transverse, time-dependent structured-light force. By applying the force in a plane orthogonal to the optical propagation direction, we suppress the effects of spectral crowding while preserving single-ion addressing. The scheme is compatible with arbitrary qubit encodings, provided that the qubit states experience a differential AC Stark shift. We experimentally realise high-fidelity two-qubit gates with error rates below $5\times10^{-3}$ in ion crystals containing up to 12 ions confined within a single potential well. These results establish gradient-field light-shift gates as a scalable approach to high-fidelity entangling generation in spectrally crowded trapped-ion systems.

Figures (2)

• Figure 1: a) Sketch of the addressing system. Two beams in two spatial modes (orange and blue) are overlapped on a polarizing beam splitter cube, after being respectively deflected by AODs. The blue beam, initially propagating like a Gaussian beam, is converted to a TEM$_{10}$ spatial mode with a phase plate before entering the AOD. An NA=0.6 lens focuses the two co-propagating light fields at the ions' position. b) Deflector scan. The frequency of each AOD is swept over the ion chain. Each point is the result of a Ramsey experiment, since the off-resonant light at 532nm is applied between two $\pi/2$ pulses before measuring the population. The orange peaks decrease in height from left to right due to an imperfect alignment of the laser beam. The right upper plot shows the electric fields for the two transverse motional modes. The bottom plot instead, displays the resulting intensity profile at the ions due to their interference. Depending on the phase between the two fields, the intensity peak can be on the right or on the left of the ion position, generating an alternating gradient. c) Motional spectrum around a carrier transition corresponding to measured values. The spacing between the two highest radial modes depends on the ratio between the two trapping frequencies, while for the lowest two axial modes the ratio is fixed to $\sqrt{3}$. d) Phase space picture and geometric phases. If two ions are illuminated with the two beams oscillating in phase, the $\ket{01}$ and $\ket{10}$ quantum states will be displaced and perform loops in phase space, acquiring a geometric phase, while the force on $\ket{00}$ and $\ket{11}$ cancels out.
• Figure 2: a) Parity oscillations for a single gate on a two-ion crystal. Error bars are given by $\sqrt{(1-\mathrm{P}(\phi)^2)/\mathrm{N}_{\mathrm{shots}}}$. b) Residual spin motion entanglement. Each point is the result of $\mathrm{N}_{\mathrm{shots}}=200$ measurements of the Bell state at the closure of the gate, and error bars are given due to projection noise. The error bar on the points at 0 are defined via the rule of succession, i.e. $1/(\mathrm{N}_{\mathrm{shots}}+1)$. c) Gate infidelity vs chain length. Each point for $N>2$ is estimated by averaging the infidelities of gates performed on the innermost and outermost ion pairs. The fidelity in each configuration is extracted from an exponential decay fit to the fidelity of 1, 3, 5, 7 and 9 concatenated gates, in order to account for state-preparation and measurement (SPAM) errors. The orange data points are measured with $^{138}$Ba$^+$. The green point is measured by co-authors A.E. and T.F. on a $^{40}$Ca$^+$ based trapped ion system (two loops in phase space and $\mathrm{t}_{\mathrm{gate}}=120µs$).