Coherent Generation and Protection of Anticoherent Spin States

Abstract

We report the first protocol specifically designed to generate anticoherent spin-$j$ states at different orders. The protocol consists of cycles of a rotation pulse about an axis followed by a squeezing pulse in a perpendicular direction. To protect these states, we develop dynamical decoupling techniques using group-based sequence design and the dynamically corrected gate formalism. We analyze key sources of dephasing, disorder, and dipole-dipole interactions and assess the effectiveness of our methods in preserving coherence. Potential applications of the produced anticoherent spin states include quantum sensing and studies related to quantum entanglement.

Figures (13)

• Figure 1: Diagram illustrating the coupling between state multipoles (for $j=2$). Each square represents a multipole $\rho_{LM}$ of the spin state from the expansion \ref{['rhoexpansion']} (these are shown explicitly for $L=0,1$). Blue and green arrows indicate the effects of rotation ($J_y$ generator) and squeezing ($J_z^2$ generator), respectively. Red crosses denote either the absence of coupling between two multipoles or the absence of an adjacent multipole.
• Figure 2: Protocol for generating anticoherent states of order $3$ for spin $j = 3$ using $n_C=3$ cycles. The optimization is performed over all parameters ($\eta_1,\eta_2,\eta_3,\theta_2$ and $\theta_3$). Each colored rectangle represents the modulus squared of the corresponding multipole of the expansion \ref{['rhoexpansion']}. The final anticoherence measure reaches $1-\mathcal{A}_{3}<10^{-7}$.
• Figure 3: Highest anticoherence measure achieved using the pulse-based protocol for orders $t=2,3$ and $4$ (from top to bottom), shown as a function of the spin quantum number $j$ for different numbers of cycles $n_C$.
• Figure 4: Majorana representation of the states \ref{['eq:AnalyticalStates_j2']} (left) and \ref{['eq:AnalyticalStates_j3']} (right) produced by $3$ rotation-squeezing cycles.
• Figure 5: Protocol for generating a spin-$3$ AC state of order $3$ based on $n_C=3$ cycles. The control parameters used are those given in Eqs. \ref{['eq.Rot.AC2']} and \ref{['eq.Squ.AC3']}.