Tailoring Dynamical Quantum Phase Transitions via Double-Mode Squeezing Manipulation

Abstract

We propose a protocol to tailor dynamical quantum phase transitions (DQPTs) by double-mode squeezing onto the initial state in the XY chain. The effect of squeezing depends critically on the system's symmetry and parameters. When the squeezing operator breaks particle-hole symmetry (PHS), DQPTs become highly tunable, allowing one to either induce transitions within a single phase or suppress them. Remarkably, when PHS is preserved and the squeezing strength reaches $r=π/4$, a universal class of DQPTs emerges, independent of the quench path. This universality is characterized by two key features: (i) the collapse of all Fisher zeros onto the real-time axis, and (ii) the saturation of intermode entanglement to its maximum in each $(k,-k)$ modes. Moreover, the critical momenta governing the DQPTs coincide exactly with the modes attaining the maximal entanglement. At this universal point, the dynamical phase vanishes, leading to a purely geometric evolution marked by $π$-jumps in the Pancharatnam geometric phase. Our work establishes initial-state squeezing as a versatile tool for tailoring far-from-equilibrium criticality and reveals a direct link between entanglement saturation and universal nonanalytic dynamics.

Figures (4)

• Figure 1: Fisher zeros $z_{0}$ of the Loschmidt amplitude in the complex time plane for varying squeezing strengths $r, r \in [0, \frac{\pi}{2}]$. In panels (a) and (c), the squeezing direction is set to $\phi = 0$, corresponding to the presence of PHS. In contrast, panels (b) and (d) depict PHS-broken cases with $\phi = \frac{\pi}{3}$. For (a) and (b), the quench paths cross the QPT, from $h_{0} = 1.5$ to $h_{1} = 0.5$ with $\gamma = 1$, while (c) and (d) represent quenches in the FM$_{x}$ phase, from $h_{0} = 0.8$ to $h_{1} = 0.2$ (also with $\gamma = 1$). All panels use identical line labels for consistency.
• Figure 2: The rate functions for the PHS-preserved squeezing with $r = \frac{\pi}{4}$, where the critical times $t_{\mathrm{min}}^{0}$ and $t_{\mathrm{max}}^{0}$ correspond to the boundaries of Fisher zeros $z_{0}$.
• Figure 3: The contour plot of condition $\Delta(r, \phi) = \min{|\cos{2r}\cos{2\alpha_{k}}-\sin{2r}\sin{2\alpha_{k}}\sin{\phi}|}$ obtained by scanning squeezing parameters $(r,\phi)$, where the quench path for (a) is from $h_{0}=0.8$ to $h_{1}=0.2$ with $\gamma=1$ (Ising limit), and for (b) from $h_{0}=0.2$ to $h_{1}=0.8$ with $\gamma=0.1$ (XX limit).
• Figure 4: Pancharatnam geometric phase $\phi_{k}^{G}(t)$ in the system under PHS-preserved squeezing with $r = \frac{\pi}{4}$.