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=qJx2, whose corresponding maximal squeezing factor scales as
N−2/3, where
N is the atomic number. On the contrary, for the other two-axis twisting Hamiltonian
HTAT=q(Jx2−Jy2), the maximal squeezing factor scales as
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
. For proper parameters, the above 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 effective atomic resonant frequency
ω0. Surprisingly, we find that by combined with the dimensionless parameter
χ(>−1), the effective atomic resonant frequency
ω0 can enhance spin squeezing largely. These results are benefit for achieving the required spin squeezing in experiments.
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.
We propose a scheme to realize the two-axis countertwisting spin-squeezing Hamiltonian inside an optical cavity with the aid of phase-locked atom-photon coupling. By careful analysis and extensive simulation, we demonstrate that our scheme is robust against dissipation caused by cavity loss and atomic spontaneous emission, and it can achieve significantly higher squeezing than one-axis twisting. We further show how our idea can be extended to generate two-mode spin-squeezed states in two coupled cavities. Because of its easy implementation and high tunability, our scheme is experimentally realizable with current technologies.
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−2/3, 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−1. Taking into account the noise effects of spin dephasing and relaxtion, we found that the proposed approaches are robust against imperfections.
We utilize multilevel atoms trapped in a driven resonant optical cavity to produce scalable multimode squeezed states for quantum sensing and metrology. While superradiance or collective dissipative emission by itself has been typically a detrimental effect for entanglement generation in optical cavities, in the presence of additional drives it can also be used as an entanglement resource. In a recent work [B. Sundar, D. Barberena, A. M. Rey, and A. Pi\~neiro Orioli, companion paper, Phys. Rev. Lett. 132, 033601 (2024)], we described a protocol for the dissipative generation of two-mode squeezing in the dark state of a six-level system with only one relevant polarization. There we showed that up to two quadratures can be squeezed. Here, we develop a generalized analytic treatment to calculate the squeezing in any multilevel system where atoms can collectively decay by emitting light into two polarization modes in a cavity. We show that in this more general system up to four spin squeezed quadratures can be obtained. We study how finite-size effects constrain the reachable squeezing, and analytically compute the scaling with
N. Our findings are readily testable in current optical cavity experiments with alkaline-earth-like atoms.
We show how a driven-dissipative cavity coupled to a collective ensemble of atoms can dynamically generate metrologically useful spin-squeezed states. In contrast to other dissipative approaches, we do not rely on complex engineered dissipation or input states, nor do we require tuning the system to a critical point. Instead, we utilize a strong symmetry, a special type of symmetry that can occur in open quantum systems and emerges naturally in systems with collective dissipation, such as superradiance. This symmetry preserves coherence and allows for the accumulation of an atom number-dependent Berry phase which in turn creates spin-squeezed states via emergent one axis twisting dynamics. This work shows that it is possible to generate entanglement in an atom-cavity resonant regime with macroscopic optical excitations of the system, going beyond the typical dispersive regime with negligible optical excitations often utilized in current cavity-QED experiments.