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arXiv:1812.03463 · Physical Review A

Spin squeezing via one- and two-axis twisting induced by a single off-resonance stimulated Raman scattering in a cavity

Gang Liu, Ya-Ni Wang, Lifen Yan, Nian-Quan Jiang, Wei Xiong, Mingfeng Wang

Published Apr 29, 2019• 7 citations
arXivHTMLPDF

Abstract

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 $N$ 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.

DOI
10.1103/physreva.99.043840

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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∝1/N2/3\ensuremath{\propto}1/{N}^{2/3}\ensuremath∝1/N2/3 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∝1/N\ensuremath{\propto}1/N\ensuremath∝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.
The strong light–matter coupling attainable in optical cavities enables the generation of highly squeezed states of atomic ensembles. It was shown by Sørensen and Mølmer (2002 Phys. Rev. A 66 022314) how an effective one-axis twisting Hamiltonian can be realized in a cavity setup. Here, we extend this work and show how an effective two-axis twisting Hamiltonian can be realized in a similar cavity setup. We compare the two schemes in order to characterize their advantages. In the absence of decoherence, the two-axis Hamiltonian leads to more squeezing than the one-axis Hamiltonian. If limited by decoherence from spontaneous emission and cavity decay, we find roughly the same level of squeezing for the two schemes scaling as where C is the single atom cooperativity and N is the total number of atoms. When compared to an ideal squeezing operation, we find that for specific initial states, a dissipative version of the one-axis scheme attains higher fidelity than the unitary one-axis scheme or the two-axis scheme. However, the unitary one-axis and two-axis schemes perform better for general initial states.
Ultracold atoms in an ultrahigh-finesse optical cavity are a powerful platform to produce spin squeezing since photon of cavity mode can induce nonlinear spin-spin interaction and thus generate a one-axis twisting Hamiltonian HOAT=qJx2H_{\text{OAT}}=qJ_{x}^{2}HOAT​=qJx2​, whose corresponding maximal squeezing factor scales as N−2/3N^{-2/3}N−2/3, where NNN is the atomic number. On the contrary, for the other two-axis twisting Hamiltonian HTAT=q(Jx2−Jy2)H_{\text{TAT}}=q(J_{x}^{2}-J_{y}^{2})HTAT​=q(Jx2​−Jy2​), the maximal squeezing factor scales as N−1N^{-1}N−1, approaching the Heisenberg limit. In this paper, inspired by recent experiments of cavity-assisted Raman transitions, we propose a scheme, in which an ensemble of ultracold six-level atoms interacts with two quantized cavity fields and two pairs of Raman lasers, to realize a tunable two-axis spin Hamiltonian %H=q(J_{x}^{2}+χJ_{y}^{2})+ω_{0}J_{z}. For proper parameters, the above one- and two- axis twisting Hamiltonians are recovered, and the scaling of N−1N^{-1}N−1 of the maximal squeezing factor can occur naturally. On the other hand, in the two-axis twisting Hamiltonian, spin squeezing is usually reduced when increasing the effective atomic resonant frequency ω0ω_{0}ω0​. Surprisingly, we find that by combined with the dimensionless parameter χ(>−1)χ(>-1)χ(>−1), the effective atomic resonant frequency ω0ω_{0}ω0​ can enhance spin squeezing largely. These results are benefit for achieving the required spin squeezing in experiments.
We propose an approach to produce spin squeezed states of a large number of nitrogen-vacancy centers in diamond nanostructures coupled to an optical cavity. Unlike the previous squeezing method proposed by Bennett et al. [Phys. Rev. Lett. 110, 156402 (2013)], which is limited by phonon number fluctuations due to the existence of phonon-spin entanglement, our proposal can completely erase the entanglement between spins and hybrid phonon-photon mode mediating the effective spin-spin interaction, and thus achieves unitary one-axis-twisting interactions between nitrogen-vacancy centres, yielding a squeezing scaling J−2/3J^{-2/3}J−2/3, where J is the total angular momentum. We found that, under certain conditions, our method has the potential to enhance the spin-spin nonlinear interactions. We also proposed a scheme utilizing repeatedly applying the one-axis-twisting evolution to two orthogonal spin directions, which enables the transformation of the one-axis-twisting interactions into two-axis-twisting type, and therefore leads to the spin squeezing with Heisenberg-limited scaling J−1J^{-1}J−1. Taking into account the noise effects of spin dephasing and relaxtion, we found that the proposed approaches are robust against imperfections.
We propose a scheme to implement Heisenberg-limited spin squeezing in a hybrid cavity optomechanical-spin system. In our system, NNN two-level systems are coupled via Tavis-Cummings interactions to a mechanical resonator (MR) in a standard optomechanical setup. Within the dispersive coupling regime, adiabatic elimination of the optical mode induces a squeezing effect on the MR, which, in the squeezed representation, effectively transforms the collective spin operators into a Bogoliubov form. Under large detuning conditions, the phonon mode mediates interactions among the Bogoliubov collective spins, thereby enabling a two-axis twisting squeezing protocol through appropriate parameter tuning. Both theoretical analysis and numerical simulations show that in the presence of dephasing and phonon dissipation, the maximum squeezing degree asymptotically converges to a constant as NNN increases, which implies the metrological precision asymptotically approaches the standard quantum limit without parameter optimization. Nevertheless, in parameter optimization we extract a scaling relation of the optimal squeezing which surpasses existing schemes in the literature. Moreover, the optimization also leads to a considerable reduction of the preparation time for the optimal squeezing. Our work may provide insights into dissipation effects in spin squeezing and offer a potential route for high-precision quantum metrology in many-body systems.
Spin squeezing state is a critical physical resource for the realization of high-precision metrology. Here, using two ground states of atoms as pseudo spin degrees of freedom, we propose a simple scheme to create high squeezing via cavity-assisted non-resonant Raman transition. The numerical simulation results show that our scheme can achieve the same optimum squeezing and has the same advantages as the conventional two-axis counter twisting model. The scheme is robust against system dissipation and provides a feasible approach for the realization of Heisenberg limit squeezing within the reach of current experimental technologies.
Multi-mode cavities have now attracted much attention both experimentally and theoretically. In this paper, inspired by recent experiments of cavity-assisted Raman transitions, we realize a two-axis spin Hamiltonian in two cavities. This realized Hamiltonian has a distinct property that all parameters can be tuned independently. For proper parameters, the well-studied one- and two-axis twisting Hamiltonians are recovered, and the scaling of N −1 of the maximal squeezing factor can occur naturally. On the other hand, in the two-axis twisting Hamiltonian, spin squeezing is usually reduced when increasing the atomic resonant frequency ω 0 . Surprisingly, we find that by combining with the dimensionless parameter χ (> −1), this atomic resonant frequency ω 0 can enhance spin squeezing greatly. These results are beneficial for achieving the required spin squeezing in experiments.