Spin squeezing of the non-Hermitian one-axis twisting model

Abstract

In the absence of decay, the conditional dynamics for an open system is often describable by a non-Hermitian Hamiltonian. This study investigates spin squeezing (SS) in non-Hermitian one-axis twisting (OAT) model. Somewhat surprisingly, SS close to the limit of Hermitian two-axis counter twisting (TACT) Hamiltonian is achievable for some parameters, which significantly improves upon the optimal value realizable by Hermitian OAT model. The drawback is like with all conditional schemes, it takes on average longer time to evolve into steady state, and the probability of no decay or success decreases as number of atoms (spins) increases. The result above for steady state SS in non-Hermitian OAT Hamiltonian is thus limited to small systems. For other parameter regimes, however, desirable SS arrives dynamically before steady state is achieved, with greatly shortened evolution time and enhanced probability of success, while still remain significantly improved over the limit of Hermitian OAT.

Study of decoherence in a system of superconducting flux-qubits interacting with an ensemble of electrons

“…It is shown that the system amplifies the pattern of spin squeezing when the line width of the spin states are taken into account. Similar results have been found in [22]. The Authors of [22] have investigated the enhancement of spin squeezing in a non-Hermitian one-axis twisting model and its persistence in time [29].…”

“…Similar results have been found in [22]. The Authors of [22] have investigated the enhancement of spin squeezing in a non-Hermitian one-axis twisting model and its persistence in time [29]. The Authors of [23,24] have reexamined the steady-state behaviours for a spin ensemble in diamond nanostructures by exerting a controllable microwave field.…”

“…Recently, the study of quantum properties as a function of time, in open systems, has received renewed attention, particularly in relation to the properties of entanglement [21][22][23][24][25][26]. In Ref.…”

Nuclear spin squeezing via electric quadrupole interaction

“…This points out the adverse effect of dephasing in keeping the quadrupolar spin in a squeezed state. On the other hand, recent studies on non-Hermitian TAC [38], and OAT [39] models have reported rather favorable squeezing conditions with respect to their Hermitian counterparts. The discrepancy may be caused by the fact that their models involved a dissipative channel, whereas we have a nondissipative phase-damping decoherence [28].…”

“…Even though TAC has superior squeezing characteristics [33], in spinor Bose-Einstein condensates it has only been indirectly realized by transforming OAT using pulse sequences, hence in this respect these can be classified as dynamical TAC [34][35][36][37]. Very recently it has been theoretically asserted that non-Hermitian OAT in the absence of decay can reach the squeezing limit of the Hermitian TAC model [38,39].…”