A 2012 proposal by Viscor, Rubio, Birkl, Mompart, and Ahufinger showed that single-site addressing (SSA) of ultracold atoms in an optical lattice can beat the diffraction limit by position-dependent stimulated Raman adiabatic passage (SLAP): a pump laser with a node at the chosen site, combined with a Stokes laser, coherently transfers every atom between two hyperfine ground states except the one sitting at the node, so the addressing profile is set by the steepness of the intensity node rather than by the beam waist. The quantitative analysis assumed perfect spin coherence during the microsecond interaction, a unit-filled Mott insulator with atoms in the motional ground state, a mathematically perfect pump-node profile, and argued only qualitatively that spontaneous photon scattering is reduced relative to light-shift-based schemes. Whether high-fidelity sub-diffraction SLAP addressing survives realistic spin decoherence and magnetic-field noise, occupancy defects and finite temperature, imperfect node profiles, and residual scattering - the condition for using it in real experiments - has not been quantified by subsequent literature and remains open.

Background

Optical lattices - periodic arrays of microtraps made from standing-wave light - are a leading platform for quantum simulation and quantum information with ultracold neutral atoms. Many protocols require manipulating one chosen atom ('single-site addressing', SSA) without disturbing its neighbors. When the lattice spacing is well below one micron, as needed for strongly correlated regimes where tunneling competes with on-site interaction, ordinary addressing fails: a focused laser beam cannot be confined tighter than roughly half its wavelength (the diffraction limit). Demonstrated routes around this include microwave spin-flip addressing in a magnetic-field gradient, where resolution is set by the gradient rather than the optics but the spin flip takes milliseconds (Weitenberg et al., Nature 471, 319 (2011)).

Viscor et al. (Phys. Rev. A 86, 063409 (2012)) proposed a fully optical, coherent route below the diffraction limit, building on the SLAP technique ('sub-wavelength localization via adiabatic passage') introduced by Mompart, Ahufinger, and Birkl (Phys. Rev. A 79, 053638 (2009)). Each atom is modeled as a three-level 'Λ system': two ground states ∣1⟩|1\rangle and ∣3⟩|3\rangle coupled to one excited state ∣2⟩|2\rangle by a pump and a Stokes laser. In STIRAP (stimulated Raman adiabatic passage), a 'counterintuitive' pulse sequence in which the Stokes pulse precedes the pump transfers population from ∣1⟩|1\rangle to ∣3⟩|3\rangle through a dark-state superposition that ideally never populates the lossy excited state, making the transfer robust against variations of pulse parameters. In SLAP the pump beam carries a node - a line of zero intensity - positioned at the site to be addressed; such profiles can be produced by a Laguerre–Gaussian (doughnut-shaped) beam, a 'bottle beam' from interfering Gaussian beams, an absorption mask, or a spatial light modulator followed by imaging. Atoms away from the node follow the dark state and are transferred, while the atom at the node remains uncoupled from the pump and stays in ∣1⟩|1\rangle; the width of the untransferred (addressed) population peak is governed by how fast the pump intensity rises away from the node, not by the beam waist. The proposal analyzed a unit-filled Mott insulator (the lattice state with exactly one atom per site) of 87^{87}Rb, finding for example an addressing-probability full width at half maximum (Δx)SLAP≈331(\Delta x)_{\mathrm{SLAP}}\approx 331 nm for a 509 nm node width, reducible to about 101 nm by increasing the pump-to-Stokes intensity ratio, with addressing times of order tens of microseconds - three orders of magnitude faster than the microwave-gradient experiment, which also reduces exposure to photon scattering.

All of these quantitative results rest on idealizations that the authors state explicitly: no spin decoherence during the interaction time; exactly one atom per site in the harmonic ground state of its trap, with no occupancy defects, finite-temperature motional excitations, or tunneling; a perfectly dark, aberration-free pump node; and no quantitative assessment of residual spontaneous scattering and heating (although spontaneous decay of the excited level is included in the density-matrix model). How these idealizations fare in a real optical-lattice experiment - the natural-generality question of whether dark-state-based sub-wavelength addressing is a robust capability rather than an idealized construct - was left open.

Problem Statement

Quantify how robust SLAP-based single-site addressing in optical lattices is when the idealizations of the original proposal are relaxed, and thereby establish - or rule out - high-fidelity sub-diffraction single-site addressing in real optical-lattice experiments. A resolution of this question requires quantitative predictions of the addressing fidelity Px0\mathcal{P}_{x_0} (the single-atom probability that the addressed atom at the target site x0x_0 ends in its intended internal state ∣1⟩|1\rangle, every other illuminated atom being intended to end in ∣3⟩|3\rangle), the crosstalk to neighboring sites (the probability that a neighboring atom is left untransferred, i.e., fails to follow the dark-state transfer), the addressing resolution (Δx)SLAP(\Delta x)_{\mathrm{SLAP}}, and the transfer efficiency η\eta (defined in the source work as η≡Px0(1−Px1)\eta\equiv\mathcal{P}_{x_0}(1-\mathcal{P}_{x_1}), the probability that the addressed atom at x0x_0 remains in ∣1⟩|1\rangle times the probability that the atom at the neighboring site x1x_1 has been transferred), as functions of the four imperfection classes that the source work left unquantified or treated only qualitatively: (i) finite spin decoherence and magnetic-field noise over the microsecond-scale interaction; (ii) deviations from the unit-filled Mott-insulator state - site-occupancy defects, finite-temperature motional excitations, and residual tunneling; (iii) realistic pump-node spatial profiles - finite node contrast, optical aberrations, and technical intensity noise - for node-forming methods such as Laguerre–Gaussian beams, bottle beams, reimaged masks, or spatial-light-modulator patterns; and (iv) residual spontaneous photon scattering and heating beyond the excited-state decay already included in the source density-matrix model - in particular photon-recoil heating of the motional states and scattering channels outside the three-level Λ\Lambda system - in the relevant parameter regimes. Predictions should state the lattice and atomic configuration used; the configuration analyzed in the source proposal (a two-dimensional 87^{87}Rb lattice with λ=1064\lambda=1064 nm lattice light at depth V0=15ErV_0=15E_r, addressing fields at λL=795\lambda_L=795 nm on the D1 line, wide Stokes waist wS=32λLw_S=32\lambda_L, and pump-node width wP=λLw_P=\lambda_L) provides the natural baseline for comparison. The single overarching objective uniting these deliverables is a validated account of whether the four imperfection classes, individually and jointly, still permit coherent SLAP addressing of one chosen atom among its neighbors, including identification of the parameter regimes where it survives and the fidelity limits where it fails.

Take high-fidelity addressing to mean an addressing fidelity Px0\mathcal{P}_{x_0} and a transfer efficiency η\eta both of at least 0.99 together with an addressing resolution (Δx)SLAP(\Delta x)_{\mathrm{SLAP}} below the diffraction limit (about half the addressing wavelength); a resolution of the question requires all four observables to be reported for each of the four imperfection classes, both individually and jointly (with all four imperfection classes present simultaneously), together with identification of the parameter regimes where addressing survives and the fidelity limits where it fails over a clearly-stated representative parameterization of the imperfection parameters of classes (i)-(iv); the transfer efficiency η\eta is a derived quantity fixed by the addressing fidelity and the crosstalk, so reporting those two already determines it; and a decisive negative finding confined to a single class does not by itself resolve the task.

References

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