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arXiv:1707.09776 · Europhysics Letters (EPL)

Spin-squeezed atomic crystal

Dariusz Kajtoch, Emilia Witkowska, Alice Sinatra

Published Aug 24, 2018• 21 citations
arXivHTMLPDF

Abstract

We propose a method to obtain a regular arrangement of two-level atoms in a three-dimensional optical lattice with unit filling, where all the atoms share internal state coherence and metrologically useful quantum correlations. Such a spin-squeezed atomic crystal is obtained by adiabatically raising an optical lattice in an interacting two-component Bose-Einstein condensate. The scheme could be directly implemented on a microwave transition with state-of-the-art techniques and used in optical-lattice atomic clocks with bosonic atoms to strongly suppress the collisional shift and benefit from the spins quantum correlations at the same time.

DOI
10.1209/0295-5075/123/20012

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Squeezed states, a special kind of entangled states, are known as a useful resource for quantum metrology. In interferometric sensors they allow to overcome the "classical" projection noise limit stemming from the independent nature of the individual photons or atoms within the interferometer. Motivated by the potential impact on metrology as wells as by fundamental questions in the context of entanglement, a lot of theoretical and experimental effort has been made to study squeezed states. The first squeezed states useful for quantum enhanced metrology have been proposed and generated in quantum optics, where the squeezed variables are the coherences of the light field. In this tutorial we focus on spin squeezing in atomic systems. We give an introduction to its concepts and discuss its generation in Bose-Einstein condensates. We discuss in detail the experimental requirements necessary for the generation and direct detection of coherent spin squeezing. Two exemplary experiments demonstrating adiabatically prepared spin squeezing based on motional degrees of freedom and diabatically realized spin squeezing based on internal hyperfine degrees of freedom are discussed.
Squeezed states, special kinds of entangled states, are known as a useful resource for quantum metrology. In interferometric sensors, they allow us to overcome the ‘classical’ projection noise limit stemming from the independent nature of the individual photons or atoms within the interferometer. Motivated by the potential impact on metrology as well as by fundamental questions in the context of entanglement, a lot of theoretical and experimental effort has been made to study squeezed states. The first squeezed states useful for quantum-enhanced metrology have been proposed and generated in quantum optics, where the squeezed variables are the coherences of the light field. In this tutorial, we focus on spin squeezing in atomic systems. We give an introduction to its concepts and discuss its generation in Bose–Einstein condensates. We discuss in detail the experimental requirements necessary for the generation and direct detection of coherent spin squeezing. Two exemplary experiments demonstrating adiabatically prepared spin squeezing based on motional degrees of freedom and diabatically realized spin squeezing based on internal hyperfine degrees of freedom are discussed.
Quantum control of many body atomic spins is often pursued in the context of an atom-light quantum interface, where a quantized light field acts as a "quantum bus" that can be used to entangle distant atoms. One key challenge is to improve the coherence of the atom-light interface and the amount of atom-light entanglement it can generate, given the constraints of working with multilevel atoms and optical fields in a 3D geometry. We have explored new ways to achieve this, through rigorous optimization of the spatial geometry, and through control of the internal atomic state. Our basic setup consists of a quantized probe beam passing through an atom cloud held in a dipole trap, first generating spin-probe entanglement through the Faraday interaction, and then using backaction from a measurement of the probe polarization to squeeze the collective atomic spin. The relevant figure of merit is the metrologically useful spin squeezing determined by the enhancement in the resolution of rotations of the collective spin, relative to the commonly used spin coherent state. With an optimized free-space geometry, and by using a 2-color probe scheme to suppress tensor light shifts, we achieve 3(2) dB of metrologically useful spin squeezing. We can further increase atom-light coupling by implementing internal state control to prepare spin states with larger initial projection noise relative to the spin coherent state. Under the right conditions this increase in projection noise can lead to stronger measurement backaction and increased atom-atom entanglement. With further internal state control the increased atom-atom entanglement can then be mapped to a basis where it corresponds to improved squeezing of, e.g., the physical spin-angular momentum or the collective atomic clock pseudospin. In practice, controlling the collective spin of N ~ 10⁶ atoms in this fashion is an extraordinarily difficult challenge because errors in the control of individual atoms tend to be highly correlated. By employing precise internal state control, we have prepared and detected projection noise limited "cat" states (which have initial projection noise that is larger by a factor of 2f = 8 for Cs relative to the spin coherent state) and estimate that we can generate up to 6.0(5) dB of metrologically useful spin squeezing, demonstrating the advantage of using the internal atomic structure as a resource for ensemble control.
We investigate the generation of entanglement (spin squeezing) in an optical-transition atomic clock through the coupling to an optical cavity in its vacuum state. We show that if each atom is prepared in a superposition of the ground state and a long-lived electronic excited state, and viewed as a spin-1/2 system, then the collective vacuum light shift entangles the atoms, resulting in a squeezed distribution of the ensemble collective spin, without any light applied. This scheme reveals that even an electromagnetic vacuum can constitute a useful resource for entanglement and quantum manipulation. By rotating the spin direction while coupling to the vacuum, the scheme can be extended to implement two-axis twisting resulting in stronger squeezing.