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arXiv:2601.16328

Bichromatic Tweezers for Qudit Quantum Computing in ${}^{87}$Sr

Enrique A. Segura Carrillo, Eric J. Meier, Michael J. Martin

physics.atom-phquant-phSubmitted Jan 22, 2026• Announced Jan 26, 2026• 0 citations
v1 · Jan 22, 2026v2 · May 6, 2026
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Abstract

Neutral atoms have become a competitive platform for quantum metrology, simulation, sensing, and computing. Current magic trapping techniques are insufficient to engineer magic trapping conditions for qudits encoded in hyperfine states with $J \neq 0$, compromising qudit coherence. In this paper we propose a scheme to engineer magic trapping conditions for qudits via bichromatic tweezers. We show it is possible to suppress differential light shifts across all magnetic sublevels of the $5s5p$ $\mathrm{^{3}P_2}$ state by using two carefully chosen wavelengths (with comparable tensor light shift magnitude and opposite sign) at an appropriate intensity ratio, thus suppressing light-shift induced dephasing, enabling scalar magic conditions between the ground state and $5s5p$ $\mathrm{^{3}P_2}$, and tensor magic conditions for qudits encoded within it. Furthermore, this technique enables robust operation at the tensor magic angle 54.7$^\circ$ with linear trap polarization via reduced sensitivity to uncertainty in experimental parameters. We expect this technique to enable new loading protocols, enhance cooling efficiency, and enhance nuclear spins' coherence times, thus facilitating qudit-based quantum computing in ${}^{87}$Sr in the $5s5p$ $\mathrm{^{3}P_2}$ manifold.

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Bichromatic Tweezers for Qudit Quantum Computing in 87{}^{87}87Sr
Neutral atoms have become a competitive platform for quantum metrology, simulation, sensing, and computing. Current magic trapping techniques are insufficient to engineer magic trapping conditions for qudits encoded in hyperfine states with J≠0J \neq 0J=0, compromising qudit coherence. In this paper we propose a scheme to engineer magic trapping conditions for qudits via bichromatic tweezers. We show it is possible to suppress differential light shifts across all magnetic sublevels of the 5s5p5s5p5s5p 3P2\mathrm{^{3}P_2}3P2​ state by using two carefully chosen wavelengths (with comparable tensor light shift magnitude and opposite sign) at an appropriate intensity ratio, thus suppressing light-shift induced dephasing, enabling scalar magic conditions between the ground state and 5s5p5s5p5s5p 3P2\mathrm{^{3}P_2}3P2​, and tensor magic conditions for qudits encoded within it. Furthermore, this technique enables robust operation at the tensor magic angle 54.7∘^\circ∘ with linear trap polarization via reduced sensitivity to uncertainty in experimental parameters. We expect this technique to enable new loading protocols, enhance cooling efficiency, and enhance nuclear spins' coherence times, thus facilitating qudit-based quantum computing in 87{}^{87}87Sr in the 5s5p5s5p5s5p 3P2\mathrm{^{3}P_2}3P2​ manifold.
Quantum systems with more than two levels - so-called qudits - offer increased computational density and reduced circuit complexity compared to qubit-based architectures, but achieving universal and scalable control remains challenging. We propose an all-optical scheme for universal qudit control in trapped neutral atoms in moderate to high magnetic fields, focusing on the fermionic isotope 173Yb (I = 5/2). The strong hyperfine interaction in the 3P1 manifold enables fast and selective Raman transitions between nuclear-spin states in the 1S0 ground-state manifold using a single linearly polarized laser. For each neighboring transition in the qudit manifold, we identify a magic polarization angle that enables coherent, state-selective control while suppressing off-resonant excitations, with operation frequencies exceeding 100 kHz. Combined with phase-shift operations, this provides universal control of the full single-qudit space. We further discuss compatible two-qudit gates based on the Rydberg blockade mechanism, completing a universal gate set, and analyze state-selective readout schemes compatible with the proposed protocol. Our results identify 173Yb as a promising platform for high-fidelity, all-optical qudit-based quantum information processing.
Optical tweezer arrays trapping ultracold atoms and molecules are a versatile quantum science platform with broad impact in quantum simulation, quantum computation, and quantum metrology. The polarization dependence of anisotropic vector and tensor light shifts offers a degree of freedom for precise quantum state engineering of trapped particles. Similarly, state-selective operations depend on the polarization of the addressing light through the atom--light coupling strength. Yet, methods for controlling the polarization of individual tweezers or local addressing beams remain an experimental challenge. Here, we demonstrate independent, site-resolved linear polarization rotation across an optical tweezer array by exploiting the local birefringence tunability of a spatial light modulator. Applying this capability to an array of 88Sr^{88}\rm{Sr}88Sr atoms, we homogenize differential light shifts imparted by the 813-nm tweezers to the narrow 1S0↔3P1{^1{\rm S}_0}\leftrightarrow{^3{\rm P}_1}1S0​↔3P1​ transition, enabling sideband cooling under a magic-angle condition. Furthermore, we show dynamic transport of trapped atoms across distinct polarization zones with high survival and preserved coherence. Finally, we characterize tweezer polarization noise and demonstrate closed-loop stabilization referenced to the atomic transition frequency, reaching mrad-level stability. Our work establishes a technique for manipulating polarization-sensitive atomic and molecular transitions in tweezer architectures, with immediate applications to optical tweezer clocks and multi-zone quantum processors.
We present a general method for engineering qudits through individually addressable transitions between Zeeman sublevels, achieved by combining a large linear Zeeman shift with a state-dependent light shift. This approach lifts the degeneracy between adjacent states while simultaneously tuning their energy splittings into the radio-frequency (RF) domain, enabling coherent manipulation within the Zeeman manifold using experimentally accessible drive frequencies. As a concrete realization, we investigate the implementation of an SU ( 5 ) encoded in the Zeeman sublevels of the long-lived P 2 3 state of neutral Sr 88 atoms confined in far-detuned, σ − -polarized optical tweezers. Using realistic experimental parameters, we numerically demonstrate full control of the manifold, including initialization into a specific SU ( 5 ) basis state via a multiphoton transfer, coherent state- and site-selective single-qudit rotations driven by RF fields, and fast state-selective optical readout. Our simulations predict state-preparation fidelities of F ≃ 0.99 within less than 1 µ s , single-qudit gate fidelities of F ≃ 0.99 with π -pulse durations of ∼ 1.4 µ s , and fast destructive imaging with durations below 10 µ s under ideal conditions. These results establish a broadly applicable framework for high-fidelity control of Zeeman sublevel-encoded qudits and highlight the P 2 3 manifold in strontium as a promising platform for scalable qudit-based quantum technologies.
Magic wavelengths and triple magic trapping conditions for 5s2 1 ⁣S05s^2~^1\!S_05s2 1S0​ and 5s5p 3 ⁣P0,25s5p~^3\!P_{0,2}5s5p 3P0,2​ states of Sr atoms
The static and dynamic electric dipole polarizabilities of the 5s2 1 ⁣S05s^2~^1\!S_05s2 1S0​ and 5s5p 3 ⁣P0,25s5p~^3\!P_{0,2}5s5p 3P0,2​ states of Sr atoms are calculated using the relativistic configuration interaction plus the many-body perturbation theory (RCI+MBPT) method. Magic wavelengths are determined for the transitions 5s2 1 ⁣S0→5s5p 3 ⁣P05s^2~^1\!S_0\rightarrow 5s5p~^3\!P_{0}5s2 1S0​→5s5p 3P0​, 5s2 1 ⁣S0→5s5p 3 ⁣P25s^2~^1\!S_0\rightarrow 5s5p~^3\!P_{2}5s2 1S0​→5s5p 3P2​, and 5s5p 3 ⁣P0→5s5p 3 ⁣P25s5p~^3\!P_0\rightarrow 5s5p~^3\!P_{2}5s5p 3P0​→5s5p 3P2​. A comprehensive study is conducted on the dependence of magic wavelengths on the angle between the laser polarization and the magnetic field. Furthermore, the conditions for realizing triple magic trapping at 813.4~nm for the 5s2 1 ⁣S05s^2~^1\!S_05s2 1S0​, 5s5p 3 ⁣P05s5p~^3\!P_{0}5s5p 3P0​ and 5s5p 3 ⁣P25s5p~^3\!P_{2}5s5p 3P2​ states are investigated. In the case of linearly polarized light, when the angle (θpθ_pθp​) between the laser polarization direction and the magnetic field is 79.1(0.7)∘79.1(0.7)^\circ79.1(0.7)∘, triple magic trapping for the 5s2 1 ⁣S05s^2~^1\!S_05s2 1S0​, 5s5p 3 ⁣P05s5p~^3\!P_{0}5s5p 3P0​, and 5s5p 3 ⁣P2 M=05s5p~^3\!P_{2}~M=05s5p 3P2​ M=0 states can be achieved. This result agrees well with the recent experimental measurement (78.49(3)∘^\circ∘)[Phys. Rev. Lett. 135, 143401 (2025)]. Meanwhile, triple magic trapping involving the 5s5p 3 ⁣P2 M=25s5p~^3\!P_{2}~M=25s5p 3P2​ M=2 state can be achieved when θp=37.4(0.3)∘θ_p= 37.4(0.3)^\circθp​=37.4(0.3)∘. The conditions for achieving triple magic trapping with circularly and arbitrarily elliptically polarized light are also presented.
State-insensitive trapping plays a significant role in many cold atom experiments. In this technique, trapping at a specific "magic" wavelength leads to identical shifts of the ground and excited states of a particular transition. Hence, the internal state of the trapped atoms remains essentially unaffected by the trapping light. This leads to increased coherence times and loading efficiency, and allows for the use of free-space manipulation techniques. However, the applicability of state-insensitive trapping is limited in terms of light sources available, with restrictions coming from either the required frequency or power. In this thesis, state-insensitive trapping of caesium atoms is considered. It can be achieved at the wavelength of 935.6 nm. However, the present work shows that this wavelength is impractical for experimental realizations of atom trapping in free space due to lack of laser sources with sufficiently high power. We therefore propose bichromatic trapping, as produced by two independent laser fields with different frequencies, to overcome the limitations related to monochromatic trapping. We show that bichromatic trapping extends the range of possible magic wavelengths compared to the specific magic wavelength associated with monochromatic trapping. Specifically, we present results for the magic wavelength combinations for caesium atoms with particular attention to the frequency range of currently available laser sources. Simultaneous state-independent trapping of atomic mixtures of caesium with rubidium and lithium atoms was also investigated, and appropriate magic wavelength combinations were identified. Additionally, species-selective state-independent trapping of atomic mixtures of caesium and lithium was explored and common wavelength pairs for tune-out and magic wavelengths of these atoms were determined.
We demonstrate that the coherence of a single mobile atomic qubit can be well preserved during a transfer process among different optical dipole traps (ODTs). This is a prerequisite step in realizing a large-scale neutral atom quantum information processing platform. A qubit encoded in the hyperfine manifold of an ^{87}Rb atom is dynamically extracted from the static quantum register by an auxiliary moving ODT and reinserted into the static ODT. Previous experiments were limited by decoherences induced by the differential light shifts of qubit states. Here, we apply a magic-intensity trapping technique which mitigates the detrimental effects of light shifts and substantially enhances the coherence time to 225±21 ms. The experimentally demonstrated magic trapping technique relies on the previously neglected hyperpolarizability contribution to the light shifts, which makes the light shift dependence on the trapping laser intensity parabolic. Because of the parabolic dependence, at a certain "magic" intensity, the first order sensitivity to trapping light-intensity variations over ODT volume is eliminated. We experimentally demonstrate the utility of this approach and measure hyperpolarizability for the first time. Our results pave the way for constructing scalable quantum-computing architectures with single atoms trapped in an array of magic ODTs.