Nuclear spin squeezing via electric quadrupole interaction

Abstract

Control over nuclear spin fluctuations is essential for processes that rely on preserving the quantum state of an embedded system. For this purpose, squeezing is a viable alternative, so far that has not been properly exploited for the nuclear spins. Of particular relevance in solids is the electric quadrupole interaction (QI), which operates on nuclei having spin higher than 1/2. In its general form, QI involves an electric field gradient (EFG) biaxiality term. Here, we show that as this EFG biaxiality increases, it enables continuous tuning of single-particle squeezing from the one-axis twisting to the two-axis countertwisting limits. A detailed analysis of QI squeezing is provided, exhibiting the intricate consequences of EFG biaxiality. The initial states over the Bloch sphere are mapped out to identify those favorable for fast initial squeezing, or for prolonged squeezings. Furthermore, the evolution of squeezing in the presence of a phase-damping channel and an external magnetic field are investigated. We observe that dephasing drives toward an anti-squeezed terminal state, the degree of which increases with the spin angular momentum. Finally, QI squeezing in the limiting case of a two-dimensional EFG with a perpendicular magnetic field is discussed, which is of importance for two-dimensional materials, and the associated beat patterns in squeezing are revealed.

Cat-state generation and stabilization for a nuclear spin through electric quadrupole interaction

“…Even though we shall be using this full Lindblad set, it can be readily verified that in the weak damping limit the Lindblad operators reduce to a single one √ γIÎ z , as considered in Ref. [31].…”

“…Since we shall not consider any other steady term in the Hamiltonian, f Q will serve for setting the time scale of the dynamics; typical values will be stated when we discuss decoherence processes. The magnitude of spin angular momentum vector I is conserved, and as in our prior work [31], this term can be dropped from dynamics at will. Note that we parametrize the Hamiltonian with respect to η = (V xx − V yy ) /V zz which defines the degree of biaxiality of the EFG [28,29], and as we shall see, plays a central role for the cat-state generation and stabilization.…”

“…Note that we parametrize the Hamiltonian with respect to η = (V xx − V yy ) /V zz which defines the degree of biaxiality of the EFG [28,29], and as we shall see, plays a central role for the cat-state generation and stabilization. It is confined to the range [0, 1]: the lower limit corresponds to a cylindrically symmetric EFG distribution, while the upper limit η = 1 can be realized, for instance, in two-dimensional materials [31].…”

“…In this work our aim is to present a simple means to generate different kinds of cat states on a single nuclear spin by harnessing the quadrupole interaction (QI) [28,29] which intrinsically operates on the quadrupolar nuclei, that is, with spin quantum number greater than 1/2. Motivated by a recent experimental exposition of squeezing with spin-7/2 nuclei [30], this work builds upon our prior study where we have shown that the generic QI supports continuous tuning of squeezing from one-axis to two-axis countertwisting limits [31]. We confine ourselves to the spin values between 1 and 9/2 that correspond to the range of abundant isotopes of quadrupolar nuclei.…”

Analogies of the classical Euler top with a rotor to spin squeezing and quantum phase transitions in a generalized Lipkin-Meshkov-Glick model

“…Based on proposals specifying various mechanisms (e.g., [4,36,39,41,46]) it was observed experimentally in hyperfine states of individual atoms [42,43], in collective spins of atomic samples interacting by spin-dependent collisions [37,44,47,48], and by optically mediated dispersive interaction in near-resonant cavities [49]. Other proposals for OAT realization include nuclear spins in quantum dots [51,64], phonon-induced interactions of spins in diamond nanostructures [53], or cold paramagnetic molecules [61].…”