The creation and manipulation of quantum entanglement is central to improving precision measurements. A principal method of generating entanglement for use in atom interferometry is the process of spin squeezing whereupon the states become more sensitive to
SU(2) rotations. One possibility to generate this entanglement is provided by one-axis twisting (OAT), where a many-particle entangled state of one degree of freedom is generated by a nonlinear Hamiltonian. We introduce a method which goes beyond OAT to create squeezing and entanglement across two distinct degrees of freedom. We present our work in the specific physical context of a system consisting of collective atomic energy levels and discrete collective momentum states, but also consider other possible realizations. Our system uses a nonlinear Hamiltonian to generate dynamics in
SU(4), thereby creating the opportunity for dynamics not possible in typical
SU(2) one-axis twisting. This leads to three axes undergoing twisting due to the two degrees of freedom and their entanglement, with the resulting potential for a more rich context of quantum entanglement. The states prepared in this system are potentially more versatile for use in multiparameter or auxiliary measurement schemes than those prepared by standard spin squeezing.
Two well-known mechanisms, one-axis twisting (OAT) and two-axis countertwisting (TACT), generate spin-squeezed states dynamically. The latter provides better spin squeezing (SS) but has not been demonstrated as the form of its interaction does not occur naturally in known physical systems. Several proposals for realizing effective TACT transformed from OAT require stringent experimental conditions in order to overcome the resulting nonstationary (oscillating) SS and continuously varying mean spin directions. This work presents a simple scheme that solves both problems by freezing SS at an optimal point and realizing effectively persistent SS by inhibiting further squeezing dynamics. Explicit procedures are outlined for persistent SS of the TACT limit. Protocols based on our scheme favorably relax experimental demands, which significantly brighten the prospects for realizing TACT.
We propose an efficient yet simple protocol to generate arbitrary symmetric entangled states with only global single-qubit rotations in a torn Hilbert space. The system is based on spin-1/2 qubits in a resonator such as atoms in an optical cavity or superconducting qubits coupled to a main bus. By sending light or microwave into the resonator, it induces ac Stark shifts on particular angular-momentum eigenstates (Dicke states) of qubits. Then we are able to generate barriers that hinder transitions between adjacent Dicke states and tear the original Hilbert space into pieces. Therefore, a simple global single-qubit rotation becomes highly nontrivial, and thus generates entanglement among the many-body system. By optimal control of energy shifts on Dicke states, we are able to generate arbitrary symmetric entangled states. We also exemplify that we can create varieties of useful states with near-unity fidelities in only one or very few steps, including W states, spin-squeezed states (SSSs), and Greenberger-Horne-Zeilinger states. Particularly, the SSS can be created by only one step with a squeezing parameter ξ R 2 ∼ 1 / N 0.843 approaching the Heisenberg limit. Our finding establishes a way for universal entanglement generations with only single-qubit drivings where all the multiple-qubit controls are integrated into simply switching on or off microwave. It has direct applications in the variational quantum optimizer, which is available with existing technology. Published by the American Physical Society 2024
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 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.
One-axis twisting (OAT) interaction is a pivotal resource for manipulating quantum states of atomic ensembles, enabling spin squeezing, atomic-cat-state generation, and weak-phase amplification. Current implementations of OAT dynamics predominantly rely on the Tavis-Cummings model of light-atoms coupling; however, this approach inevitably introduces an additional Stark term that entangles the light with the atoms, which compromises the unitarity of OAT evolution and thereby degrades the OAT-based control precision. Here we propose a scheme based on a driven Tavis-Cummings model to achieve near-unitary OAT evolution. We demonstrate that both constant and time-varying driving of an atoms-cavity hybrid system can realize near-unitary OAT evolution, albeit with distinct coupling strength. Furthermore, when atomic dissipation is taken into account, we find that the time-varying-driving scheme exhibits superior resistance to decoherence. Our approach is broadly applicable to a variety of atomic platforms, including cold atoms, trapped ions, and nitrogen-vacancy centers.