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.
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.
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.
In two-component Bose-Einstein condensates, the one-axis twisting Hamiltonian leads to spin squeezing with a limitation that scales with the number of atoms as ${N}^{\ensuremath{-}2/3}$. We propose a scheme to transform the one-axis twisting Hamiltonian into a two-axis twisting Hamiltonian, resulting in enhanced spin squeezing proportional to ${N}^{\ensuremath{-}1}$ approaching the Heisenberg limit. Instead of pulse sequences, only one continuous driving field is required to realize such a transformation, thus the scheme is promising for experimental realization of a two-axis twisting Hamiltonian. Quantum information processing and quantum metrology may benefit from this method in the future.
An advantageous architecture for producing deterministic spin squeezing is cavity QED. We show that the recently discovered one photon - two atom excitation process can be used to generate optimal squeezing (scaling as
1/N) of an ensemble of
N spins coupled to a single-mode cavity. This method has some remarkable features. It is a resonant phenomenon mediated by real photons, which provides the advantage of tunability. This allows to create a sizeable squeezing already at the single-photon limit. Finally, in the strong cavity-driving regime the effective theory is similar to a two-axis Hamiltonian. We calculate that reaching
−30dB is possible already with the known reported spin-cavity and decoherence rates in magnetic molecules coupled to superconducting circuit resonators. This system represents an attractive on-chip architecture for the realization of technological solutions in sensing.