Quantum science with arrays of metastable helium-3 atoms

TL;DR

The paper introduces a blueprint for quantum science with programmable optical tweezer arrays using metastable helium-3 ($^3$He$^*$), the lightest trappable fermion, to dramatically speed up motional and transport dynamics. It presents a realistic platform that leverages the unique level structure and Rydberg interactions of $^3$He$^*$ to realize fast inter-tweezer hopping, robust hyperfine qubits at a magic field, and motional qubits encoded in the trap potential, all while enabling high-fidelity Rydberg entangling gates. The work provides concrete analyses of trapping wavelengths, polarizabilities, Raman sideband cooling, and measurement-based cooling, supported by detailed calculations of Lamb-Dicke parameters, optical-pumping schemes, and the $eta$-ratio fidelity limit for Raman transitions. It then articulates compelling applications to fermionic quantum simulation and computing, including native fermionic SWAP and CZ gates, Trotterized FH-type models, multi-orbital and moiré physics, and 3D single-site-resolved simulations, with extensions to lattice gauge theories and quantum chemistry beyond the Born-Oppenheimer approximation. Beyond computation, the framework offers avenues for precision measurements and fundamental physics via clock transitions and isotope shifts in metastable helium, highlighting the broad potential of $^3$He$^*$ arrays for both quantum information and fundamental studies.

Abstract

The motion of atoms in programmable optical tweezer arrays offers many new opportunities for neutral atom quantum science. These include inter- and intra-site atom motion for resource-efficient implementations of fermionic and bosonic modes, respectively, as well as tweezer transport for efficient compilation of arbitrary circuits. However, the exploitation of atomic motion for all three purposes and others is limited by the inertia of the atoms. We present a comprehensive architectural blueprint for the use of fermionic metastable helium-3 ($^3$He$^*$) atoms -- the lightest trappable atomic species -- in programmable optical tweezer arrays. This includes a concrete analysis of atomic structure considerations as well as Rydberg-mediated interactions. We show that inter-tweezer hopping of $^3$He$^*$ atoms can be $\gtrsim3\times$ faster than previous demonstrations with lithium-6. We also demonstrate a new toolbox for encoding and manipulating qubits directly in the tweezer trap potential, uniquely enabled by the light mass of $^3$He$^*$. Finally, we provide several examples of new opportunities for fermionic quantum simulation and computation that leverage the transport and inter-tweezer hopping of $^3$He$^*$ atom arrays. These tools present new methods to improve the resource efficiency of neutral atom quantum science that may also enable quantum simulations of lattice gauge theories and quantum chemistry outside the Born-Oppenheimer approximation

Figures (15)

• Figure 1: Advantages of small mass for quantum science applications. (a) The trap frequency of an atom in a tweezer scales as $\omega\sim m^{-1/2}$. (b) For fermionic hopping operations, the tunneling rate scales as $t\sim m^{-1}$ for the same trap depth in recoil units $E_R$. (c) A large trap frequency enables bosonic encodings with Raman sideband drives and/or direct trap modulation. (d) The trap frequency also sets the limit on tweezer acceleration during coherent transport, so light atoms enable faster transport.
• Figure 2: Relevant level structure for $^3$He*. (a) The level diagram including the absolute ground state $1s^2$$^1S_0$; the $1s2s$$^3S_1$ "metastable ground" state; the $1s2s$$^1S_0$ "clock" state; the $1s2p$$^3P_J$ manifold for cooling, optical pumping, and Raman coupling; and the $1s3p$$^3$P$_J$ manifold that will be used for fluorescence readout. (b) A zoom-in of the $1s2s$$^3S_1$ and $^3P_J$ transition with wavelength 1083 nm. This system defines the qubit, sideband cooling and motion-qubit coupling, and optical pumping. Note the large separation between $^3P_0$ and $^3P_1$/$^3P_2$ and the lack of hyperfine structure in the former.
• Figure 3: The optical polarizability of key states. (a) The polarizability of the ground state (green), upper state of optical pumping (orange), and excited state for fluorescence detection (light blue) as a function of wavelength, where the upper panel shows a zoom-in around the target wavelengths of 1013 and 1150 nm for blue- and red-detuned tweezer trapping, respectively, indicated by dashed lines. (b) The proposed scheme for fluorescence detection via the $1s3p$$^3P_2$ level that is coupled to the $1s2s$$^3S_1$ manifold with a favorable branching fraction and suitable wavelength (389 nm) for detection on a silicon camera. For detail on the polarizability calculation, see Appendix \ref{['Appendix, He polarizability']}.
• Figure 4: The schematic approach for Raman sideband cooling. (a) Optical pumping (OP) that should preserve the motional state $|n\rangle$. (b) Raman transitions between two ground states (one of which is the dark state of OP) that reduce $|n\rangle$. OP and the Raman sideband pulses are applied in alternation. (c) Interplay between probability of occupying motional ground state (red) and off-resonant scattering rate from trap $\mathrm{R_{sc}}$ (blue), both as functions of tweezer power/depth (assuming a tweezer waist of $w_0\approx1\mu$m). The red solid line represents $(1-(\eta_r^\text{OP})^2)^2(1-(\eta_z^\text{OP})^2)$ while the red dashed line represents $(1-(\eta_r^\text{OP})^2)^3$. Although the off-resonant scattering rate increases with increase in trap depth/power, as needed to achieve higher ground state probability, this trap scattering rate is still slow compared to the expected cooling rate. (d) Interplay between “good” to “bad” decay ratio $\Gamma_\mathrm{gg}/\Gamma_\mathrm{ge}$ and OP scattering rate $\Gamma_\mathrm{gg}$, both as functions of OP detuning $\Delta$. To avoid the anti-trapped excited state, finite OP detuning is utilized to realize a dressed state regime, such that the spontaneous decay happens predominantly between trapped dressed states (“good” decays), while still maintaining relatively fast OP scattering rate.
• Figure 5: Measurement-based cooling with a tunnel-coupled auxiliary tweezer. An auxiliary tweezer (red) captures a thermal error from the science tweezer (blue) by adiabatically ramping through resonance (see text). Then, the auxiliary tweezer is separated and moved to a readout zone, where a fluorescence image reveals which science tweezer hosted an error.