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Physical Review A

Squeezed spin states

Masahiro Kitagawa, Masahito Ueda

Published Jun 1, 1993• 1,740 citations
Publisher

Abstract

The basic concept of squeezed spin states is established and the principles for their generation are discussed. Two proposed mechanisms, referred to as one-axis twisting and two-axis countertwisting, are shown to reduce the standard quantum noise S/2 of the coherent S-spin state down to 1/2(S/3${)}^{1/3}$ and 1/2, respectively. Implementations of spin squeezing in interferometers are also discussed.

DOI
10.1103/physreva.47.5138

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The basic concept of squeezed spin states is established and the principles for their generation are discussed. Two proposed mechanisms, referred to as one-axis twisting and two-axis countertwisting, are shown to reduce the standard quantum noise S/2 of the coherent S-spin state down to 1/2(S/3)1/3{)}^{1/3})1/3 and 1/2, respectively. Implementations of spin squeezing in interferometers are also discussed.
Squeezed spin states possess unique quantum correlation or entanglement and are significantly promising for advancing quantum information processing and quantum metrology. In recent back-to-back publications [C. Gross et al., Nature (London) 464, 1165 (2010) and Max F. Riedel et al., Nature (London) 464, 1170 (2010)], reduced spin fluctuations are observed leading to spin squeezing at -8.2 and -2.5 dB, respectively, in two-component atomic condensates exhibiting one-axis-twisting interactions. The noise reduction limit for the one-axis twisting scales as ∝1/N(2/3), which for a condensate with N∼10(3) atoms is about 100 times below the standard quantum limit. We present a scheme using repeated Rabi pulses capable of transforming the one-axis-twisting spin squeezing into the two-axis-twisting type, leading to Heisenberg limited noise reduction ∝1/N or an extra tenfold improvement for N∼10(3).
Squeezed spin states have important applications in quantum metrology and sensing. It has been shown by S\o{}rensen and M\o{}lmer [Phys. Rev. A 66, 022314 (2002)] that an effective one-axis-twisting interaction can be realized in a cavity setup via a double off-resonance stimulated Raman scattering, resulting in a noise reduction scaling $\ensuremath{\propto}1/{N}^{2/3}$ with NNN being the atom number. Here, we show that, by making an appropriate change of the initial input spin state, it is possible to produce a one-axis-twisting spin squeezing via a single off-resonance stimulated Raman scattering, which thus can greatly simplify the realistic implementation. We also show that the one-axis-twisting interaction can be transformed into a more efficient two-axis-twisting interaction by rotating the collective spin while coupling to the cavity, yielding a Heisenberg limited noise reduction $\ensuremath{\propto}1/N$. Considering the noise effects due to atomic decoherence and cavity decay, we find that substantial squeezing is still attainable with current laboratory techniques.
Abstract SU(1, 1) coherent and squeezed states have been widely studied in optical, hybrid atom–light, and spinor Bose–Einstein condensate experiments. Traditionally, the definition of SU(1, 1) squeezing refers to the uncertainty relationship, which implies that the SU(1, 1) coherent state is already squeezed if it is placed in an appropriate system of coordinates. In this report we investigate the basic concept of SU(1, 1) squeezing and discuss the principle for the generation of squeezed states. We establish a new definition of the squeezing criterion for the SU(1, 1) states. We study the dynamical properties in an atom–molecule system and show that the SU(1, 1) squeezed state can be generated with a nonlinear atomic interaction, which is similar to the one-axis twisting mechanism in spin squeezing. We also discuss the effect of the atomic number on squeezing, and show that the optimal squeezing and optimal squeezing angle exhibit a sudden transition at a fixed atomic number value.
Squeezing of quantum states is of great interest due to its application in high-precision measurement that can exceed standard quantum noise limit described by Heisenberg uncertainty relations. Here, we study the squeezing of quantum systems with SU(3)\text{SU}(3)SU(3) symmetry via a one-axis twisting Hamiltonian and examine the intriguing connections between the squeezing of spin-1/2 and spin-1 systems. There are seven subalgebras of su(3)\text{su}(3)su(3) Lie algebra. All these subalgebras are identical with su(2)\text{su}(2)su(2) Lie algebra but not all of them have the same anticommutation relations as su(2)\text{su}(2)su(2). Interestingly, squeezing parameters corresponding to spin-1 subalgebras depend not only on structure constants but also on anticommutation relations of the subalgebras. Our results are reported for the subalgebras with vanishing anticommutators and nematic squeezing, while in other cases our first-principle calculation recovers known results.