We show that using the process of one-axis-twist squeezing in an echo configuration, it is possible to control the orientation of the macroscopic magnetic moment of a large number of atoms by manipulating the quantum state of a single atom that is physically isolated from the ensemble. With this control technique, it is also possible to entangle an ensemble with a single atom deterministically, which mimics the thought experiment known as the Schrödinger cat. In addition, this technique would make it possible to generate a mesoscopic Schrödinger cat state for a large number of atoms far more rapidly that the conventional process for generating such a state, with an orientation that is independent of the parity of the number of atoms. Apart from the echo configuration, we have also investigated the behavior of one-axis-twist squeezing for some special values of the squeezing parameter. We find that the squeezing propagator can be expressed as the sum of n rotation operators if the product of n and the squeezing parameter equals pi, where n is a non-zero integer. A direct consequence of this property of one-axis-twist squeezing is that there is a hidden order in a squeezed state generated under this condition even if its Husimi quasi-probability distribution looks irregular.
We show that using the process of one-axis-twist squeezing in an echo configuration, it is possible to control the orientation of the macroscopic magnetic moment of a large number of atoms by manipulating the quantum state of a single atom that is physically isolated from the ensemble. With this control technique, it is also possible to entangle an ensemble with a single atom deterministically, which mimics the thought experiment known as the Schrödinger cat. In addition, this technique would make it possible to generate a mesoscopic Schrödinger cat state for a large number of atoms far more rapidly that the conventional process for generating such a state, with an orientation that is independent of the parity of the number of atoms. Apart from the echo configuration, we have also investigated the behavior of one-axis-twist squeezing for some special values of the squeezing parameter. We find that the squeezing propagator can be expressed as the sum of n rotation operators if the product of n and the squeezing parameter equals pi, where n is a non-zero integer. A direct consequence of this property of one-axis-twist squeezing is that there is a hidden order in a squeezed state generated under this condition even if its Husimi quasi-probability distribution looks irregular.
The Schrödinger cat state protocol (SCSP) makes use of a Schrödinger cat (SC) state generated with one-axis-twist squeezing (OATS) to enhance the sensitivity. In principle, the SCSP can magnify the phase shift by a factor N, the number of atoms under interrogation, accompanied by a quantum noise amplification by a factor of root-N, enabling an atomic sensor to reach the Heisenberg limit. However, the current SCSP can reach this benchmark only if the parity of N is known, which is almost impossible for a large ensemble. The reason is the orientation of the SC state generated with the conventional OATS depends on the parity of N. In this paper, we propose a modified OATS (MOATS) operation that generates the SC state aligned in a certain direction regardless of the parity of N.
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.
We present a protocol for an atomic interferometer that reaches the Heisenberg limit (HL), within a factor of $\ensuremath{\sim}\sqrt{2}$, via collective state detection and critical tuning of one-axis twist spin squeezing. It generates a Schr\"odinger cat state, as a superposition of two extremal collective states. When this Schr\"odinger-cat-state interferometer is used as a gyroscope, the interference occurs at an ultrahigh Compton frequency, corresponding to a mesoscopic single object with a mass of Nm, where N is the number of particles in the ensemble, and m is the mass of each particle. For 87Rb atoms, with N=106, for example, the interference would occur at a Compton frequency of $\ensuremath{\sim}2\ifmmode\times\else\texttimes\fi{}{10}^{31}$ Hz. Under this scheme, the signal is found to depend critically on the parity of N. We present two variants of the protocol. Under protocol A, the fringes are narrowed by a factor of N for one parity, while for the other parity the signal is zero. Under protocol B, the fringes are narrowed by a factor of N for one parity, and by a factor of N for the other parity. Both protocols can be modified in a manner that reverses the behavior of the signals for the two parities. Over repeated measurements under which the probability of being even or odd is equal, the averaged sensitivity is smaller than the HL by a factor of $\ensuremath{\sim}\sqrt{2}$ for both versions of the protocol. We describe an experimental scheme for realizing such an atomic interferometer, and discuss potential limitations due to experimental constraints imposed by the current state of the art, for both collective state detection and one-axis-twist squeezing. We show that when the Schr\"odinger-cat-state interferometer is configured as an accelerometer, the effective two-photon wave vector is enhanced by a factor of N, leading to the same degree of enhancement in sensitivity. We also show that such a mesoscopic single object can be used to increase the effective base frequency of an atomic clock by a factor of N, with a sensitivity that is equivalent to the HL, within a factor of $\ensuremath{\sim}\sqrt{2}$.
The magnon cat state represents a macroscopic quantum superposition of collective magnetic excitations of large number spins that not only provides fundamental tests of macroscopic quantum effects but also finds applications in quantum metrology and quantum computation. In particular, remote generation and manipulation of Schrödinger cat states are particularly interesting for the development of long-distance and large-scale quantum information processing. Here, we propose an approach to remotely prepare magnon even or odd cat states by performing local non-Gaussian operations on the optical mode that is entangled with the magnon mode through pulsed optomagnonic interaction. By evaluating key properties of the resulting cat states, we show that for experimentally feasible parameters, they are generated with both high fidelity and nonclassicality, as well as with a size large enough to be useful for quantum technologies. Furthermore, the effects of experimental imperfections such as the error of projective measurements and dark count when performing single-photon operations have been discussed, where the lifetime of the created magnon cat states is expected to be t∼1 μs.