#tensorlightshift

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Nuclear Spin Quantum Control In Alkaline-Earth Atoms

Nuclear Spin Quantum

The nuclear spin of alkaline-earth atoms, particularly strontium-87 (({}^{87}\text{Sr})), presents ample potential for developing quantum technologies like sensitive metrology and  quantum computing. Nuclear spin of a single ({}^{87}\text{Sr}) atom, with F=9/2 spin quantum number, has 10 spin states, unlike ordinary qubits with only two states (0 and 1). Due to its multi-state capabilities, it can operate as a “qudit,” considerably increasing the quantum information that can be encoded in a single atom.

Nuclear spin’s strong isolation from outside perturbations makes it ideal for quantum information. Due to its nuclear composition, low vector and tensor polarisabilities in the ground state, and small Landé factor, the atom is immune to stray magnetic field gradients and spin-dependent light shifts. This intrinsic robustness allows coherent superpositions to last for many seconds, resulting in extremely extended coherence times, according to researchers. We achieved a 40 ± 7 second echo coherence time (({T}{2}^{{{{\mathrm{echo}}}}})) and an estimated 21 ± 7 second Ramsey dephasing time (({T}{2}^{\star })).

High-Dimensional Coherent Control

These high-dimensional nuclear spin states require manipulation beyond spin precession (using su(2) generators) to properly utilise their quantum potential. Scientists used a complicated tensor light shift approach to do this.

The TLS generates a quadratic energy shift between Zeeman states proportional to (m_F^2) using a calibrated laser beam. Scientists can manipulate two-photon Raman resonance settings with this energy change. Careful detuning lets them coherently manage isolated spin states. Engineering unitary transformations from su(N) generators allow for more flexible spin precession control than ordinary spin precession. Experiments for coherent operations have shown high fidelity, often greater than 99% for certain states.

Two main types of Raman transitions have been identified:

(\boldsymbol{\delta}\text{mF}=\mathbf{1}) Spin-changing transitions: These transitions between neighbouring Zeeman sublevels (e.g., m_F = -5/2) and m_F = -3/2) are achieved by absorbing (\pi)-photons from the TLS beam and (\sigma^-) photons from the Raman beam. These exhibit high fidelity (0.994) for a (\pi/2) pulse.

The formula is (\boldsymbol{\delta}\text{mF}=\mathbf{2}). Modulating the Raman laser into two frequency components causes spin-changing transitions that modify nearby Zeeman sublevels (e.g., m_F = -7/2) and -3/2). While these two-level rotations are similar, they have more severe damping (fidelity ~0.90 for a (\pi/2) pulse) in recent investigations.

The experimental setup for these operations is:

Optical Tweezers: SLMs build holographic arrays that trap individual ({}^{87}\text{Sr}) atoms. “Phoenix” from Atom Computing, Inc. uses such a platform.

Two phase-coherent laser beams, the Raman beam for transitions and the TLS beam for quadratic energy shift, are created from a single source and carefully regulated using acousto-optic modulators (AOMs) and electro-optic modulators (EOMs).

Spin State Measurement: Spin-selective momentum transfer measures spin-state distribution after an experiment cycle.

Interferometry and Applications of Qudit

These high-dimensional nuclear spin states can be coherently manipulated, enabling quantum simulation and sensing.

Ramsey interferometry describes qubit coherence. Inhomogeneity and polarisation changes in the TLS beam can cause decoherence and phase noise, but turning it off adiabatically during the interferometer’s dark period reduces these effects. Long-lived coherent superpositions over seconds are observed.

Parallel Ramsey Interferometers for Multi-Parameter Sensing: This innovative method observes many external fields on atoms simultaneously. Use independent pairings of spin states in the atom’s hyperfine structure to operate two Ramsey interferometers simultaneously to detect characteristics like quadratic and linear Zeeman shifts. Parallelisation allows correlation analysis of numerous noise sources and common noise rejection, which sequential observations cannot do.

The simultaneous measurement of many non-commuting observables is generally forbidden by quantum mechanics. This solution solves the problem. During measurement, the approach coherently translates information from main qubit states into initially empty “ancillary” spin states, extending the atoms’ Hilbert space. Controlled rotations on the qubit and auxiliary states can reveal previously unobservable non-commuting observables in the extended state space’s final population measurement. This technique allows new physics investigations and better collective atomic state characterisation.

Future outlook and directions

These findings are promising, but more research is needed to optimise these systems. Cross-talk between nearby qubits, Stark-shift beam dispersion, and quasi-degeneracy prevent simultaneous control of all 10 spin states. Future efforts aim to reduce these by:

Applying stronger magnetic fields.

Using advanced pulse shaping to reduce non-resonant population transfers.

Narrower optical transitions, like the ({}^{1}\text{S}_0 \to {}^{3}\text{P}_2) transition, are being studied for TLS engineering to reduce spontaneous emission.

The goal is to increase computational array sizes and achieve quicker gate operation durations, with system coherence times 10(^8) times longer than gate lengths.

High-dimensional nuclear spins in alkaline-earth atoms like strontium-87 require these advancements for next-generation quantum sensors and universal quantum computers. Large nuclear spins with su(N) symmetry are intriguing for quantum many-body physics and offer new opportunities to study quantum magnetism.