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.
Spin squeezing generated via inter-atom entanglement in multilevel atomic ensembles provides a powerful resource for quantum-enhanced metrology. Existing schemes that harness internal atomic degrees of freedom to boost squeezing typically encode the collective squeezing in complex superpositions of magnetic sublevels, which complicates state control and limits practical applications. Here, we propose a coherent control scheme that simultaneously enhances collective spin squeezing and maps the resulting atom-atom entanglement onto two well-defined magnetic sublevels suitable for subsequent metrology experiments. Our protocol sandwiches a quantum non-demolition measurement between two internal one-axis-twisting interactions arranged in an echo sequence. We show that this approach can optimally leverage internal states to boost the inter-atom entanglement and, at the same time, encode it in two magnetic sublevels, which is readily convertible into metrologically useful spin squeezing. Our results offer a straightforward and efficient strategy for generating highly entangled yet readily accessible quantum states in multilevel atomic systems.
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.
Spin squeezing is one of the most attractive methods for realizing high-precision metrology. In this paper we propose a protocol for generating spin squeezing in an atomic ensemble via a fully quantum degenerate parametric amplifier. We discuss the properties of generating spin squeezing with and without driving the pump cavity. Numerical simulation results show that the generated spin squeezing strength is sizable and is comparable to that obtained using a two-axis twisting model. Moreover, we demonstrate that the protocol is experimentally feasible by introducing the corresponding experimental parameters. Therefore, the proposed protocol provides a promising approach to realize spin squeezing in photon-spin coupling systems.
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.
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.