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arXiv:1407.8420 · Physical Review A

Protected subspace Ramsey spectroscopy

Laurin Ostermann, David Plankensteiner, Helmut Ritsch, Claudiu Genes

Published Nov 11, 2014• 17 citations
arXivHTMLPDF

Abstract

We study a modified Ramsey spectroscopy technique employing slowly decaying states for quantum metrology applications using dense ensembles. While closely positioned atoms exhibit super-radiant collective decay and dipole-dipole induced frequency shifts, recent results [L. Ostermann, H. Ritsch, and C. Genes, Phys. Rev. Lett. 111, 123601 (2013)] suggest the possibility to suppress such detrimental effects and achieve an even better scaling of the frequency sensitivity with interrogation time than for noninteracting particles. Here we present an in-depth analysis of this ``protected subspace Ramsey technique'' using improved analytical modeling and numerical simulations including larger three-dimensional (3D) samples. Surprisingly we find that using subradiant states of $N$ particles to encode the atomic coherence yields a scaling of the optimal sensitivity better than $1/\sqrt{N}$. Applied to ultracold atoms in 3D optical lattices we predict a precision beyond the single atom linewidth.

DOI
10.1103/physreva.90.053823

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We study a modified Ramsey spectroscopy technique employing slowly decaying states for quantum metrology applications using dense ensembles. While closely positioned atoms exhibit super-radiant collective decay and dipole-dipole induced frequency shifts, recent results [L. Ostermann, H. Ritsch, and C. Genes, Phys. Rev. Lett. 111, 123601 (2013)] suggest the possibility to suppress such detrimental effects and achieve an even better scaling of the frequency sensitivity with interrogation time than for noninteracting particles. Here we present an in-depth analysis of this ``protected subspace Ramsey technique'' using improved analytical modeling and numerical simulations including larger three-dimensional (3D) samples. Surprisingly we find that using subradiant states of NNN particles to encode the atomic coherence yields a scaling of the optimal sensitivity better than 1/N1/\sqrt{N}1/N​. Applied to ultracold atoms in 3D optical lattices we predict a precision beyond the single atom linewidth.
Ramsey interferometry is routinely used in quantum metrology for the most sensitive measurements of optical clock frequencies. Spontaneous decay to the electromagnetic vacuum ultimately limits the interrogation time and thus sets a lower bound to the optimal frequency sensitivity. In dense ensembles of two-level systems, the presence of collective effects such as superradiance and dipole-dipole interaction tends to decrease the sensitivity even further. We show that by a redesign of the Ramsey-pulse sequence to include different rotations of individual spins that effectively fold the collective state onto a state close to the center of the Bloch sphere, partial protection from collective decoherence is possible. This allows a significant improvement in the sensitivity limit of a clock transition detection scheme over the conventional Ramsey method for interacting systems and even for noninteracting decaying atoms.
Laser noise is a decisive limiting factor in high precision spectroscopy of narrow lines using atomic ensembles. In an idealized Doppler and differential-light-shift-free magic wavelength lattice configuration, it remains as one distinct principal limitation beyond collective atomic decay. In this work we study the limitations originating from laser phase and amplitude noise in an idealized Ramsey pulse interrogation scheme with uncorrelated atoms. Phase noise leads to a saturation of the frequency sensitivity with increasing atom number while amplitude noise implies a scaling with τ being the interrogation time. We employ a technique using decoherence-free subspaces first introduced in Dorner (2012 New J. Phys. 14 043011 ) which can restore the scaling with the square root of the inverse particle number . Similar results and improvements are obtained numerically for a Rabi spectroscopy setup.
Ramsey spectroscopy in large, dense ensembles of ultra-cold atoms trapped in optical lattices suffers from dipole-dipole interaction induced shifts and collective superradiance limiting its precision and accuracy. We propose a novel geometry implementing fast signal readout with minimal heating for large atom numbers at lower densities via an optical cavity operated in the weak single atom but strong collective coupling regime. The key idea is controlled collective transverse π/2π/2π/2-excitation of the atoms to prepare a macroscopic collective spin protected from cavity superradiance. This requires that the two halves of the atomic ensemble are coupled to the cavity mode with opposite phase, which is naturally realized for a homogeneously filled volume covering odd and even sites of the cavity mode along the cavity axis. The origin of the superior precision can be traced back to destructive interference among sub-ensembles in the complex nonlinear collective atom field dynamics. In the same configuration we find surprising regular self-pulsing of the cavity output for suitable continuous illumination. Our simulations for large atom numbers employing a cumulant expansion are qualitatively confirmed by a full quantum treatment of smaller ensembles.
Laser noise is a decisive limiting factor in high precision spectroscopy of narrow lines using atomic ensembles. In an idealized Doppler and differential-light-shift-free magic wavelength lattice configuration, it remains as one distinct principal limitation beyond collective atomic decay. In this work we study the limitations originating from laser phase and amplitude noise in an idealized Ramsey pulse interrogation scheme with uncorrelated atoms. Phase noise leads to a saturation of the frequency sensitivity with increasing atom number while amplitude noise implies a scaling 1/root T with T being the interrogation time. We employ a technique using decoherence-free subspaces first introduced in Dorner (2012 New J. Phys. 14 043011) which can restore the scaling with the square root of the inverse particle number 1/root N. Similar results and improvements are obtained numerically for a Rabi spectroscopy setup.
When an ensemble of quantum emitters interacts with a common radiation field, their emission becomes collective, giving rise to superradiant and subradiant states, characterized by broadened and narrowed linewidths. In this work, we propose to harness subradiant states for quantum metrology; such states naturally arise in subwavelength-spaced atomic arrays in free space and in small ensembles of emitters coupled to one-dimensional waveguides. We demonstrate that their collective optical response yields sharp, narrow features in the transmittance spectrum, which can be used to enhance sensitivity to external perturbations. This improved sensitivity can be applied to atomic clock operation, spatially resolved imaging of emitter positions, and enables precise detection of both global and spatially varying detunings (such as those induced by electromagnetic fields or gravitational gradients).