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Tailoring Dynamical Quantum Phase Transitions via Double-Mode Squeezing Manipulation

This paper proposes a protocol to tailor dynamical quantum phase transitions in the XY chain via double-mode squeezing, demonstrating that breaking particle-hole symmetry enables tunable control over transitions while preserving it at a specific strength ( $r=\pi/4$ ) induces a universal class of criticality characterized by Fisher zero collapse, maximal intermode entanglement, and purely geometric evolution.

Original authors: Kaiyuan Cao, Haodong Wang, Xiang-Ping Jiang, Shu chen, Jian Wang

Published 2026-09-23

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CC BY 4.0

Original authors: Kaiyuan Cao, Haodong Wang, Xiang-Ping Jiang, Shu chen, Jian Wang

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Quantum systems are notoriously fragile, yet they hold the promise of revolutionizing how we compute, measure, and understand the universe. At the heart of this potential lies the ability to control the behavior of many particles acting together. In the quiet, cold world of quantum physics, scientists often study what happens when a system is suddenly jolted out of balance—a process known as a "quench." Imagine a calm lake that is suddenly struck by a stone; the ripples that follow tell a story about the water's properties. In the quantum realm, these ripples can undergo dramatic shifts called dynamical quantum phase transitions. Unlike the familiar freezing of water or the melting of ice, which happen when temperature changes slowly, these transitions occur in time, revealing sudden, sharp changes in how a quantum system evolves after a shock. Understanding and, more importantly, controlling these transitions is a major goal for researchers, as it could unlock new ways to manipulate quantum materials and information.

For years, scientists have observed these transitions, but they have largely been passive observers, watching how nature behaves under fixed conditions. A new study by researchers at Yangzhou University, Hangzhou Normal University, and the Chinese Academy of Sciences proposes a way to actively steer these transitions. They suggest a method to "tailor" the behavior of a quantum chain of atoms by preparing them in a specific, squeezed state before the experiment begins. In this context, "squeezing" is a technique that reshapes the uncertainty of a quantum system, much like compressing a spring to store energy in a precise way. The researchers focused on a specific type of atomic chain, known as an XY chain, and applied a double-mode squeezing operation. This means they manipulated pairs of particles moving in opposite directions simultaneously, a move that fundamentally alters the starting conditions of the experiment.

The team discovered that the outcome of this manipulation depends entirely on a hidden symmetry in the system, a property they call particle-hole symmetry. When the squeezing operation breaks this symmetry, the researchers found they could tune the timing of the quantum phase transitions with great precision. By adjusting the strength of the squeeze, they could shift the exact moment when the transition occurs, or even induce a transition in a situation where none would normally happen. Conversely, they could also suppress a transition that would have occurred naturally. This level of control turns the squeezing operation into a versatile tool, allowing scientists to design the dynamical behavior of the system rather than just watching it unfold.

However, the most striking finding emerged when the researchers preserved the system's symmetry and applied a specific, strong squeeze. They identified a unique setting where the squeezing strength reached a precise value, corresponding to a mathematical ratio of pi divided by four. At this specific point, the behavior of the system became universal. Regardless of how the experiment was set up or which path the system took after the initial shock, the result was always the same. The complex patterns of the transition collapsed into a simple, predictable line. In this state, the system's evolution was no longer driven by the accumulation of energy over time, but purely by geometry. The researchers observed that the system's state jumped abruptly between two distinct configurations, a behavior marked by sharp, sudden shifts in a geometric property of the quantum state.

This universal behavior is deeply linked to the concept of entanglement, a phenomenon where particles become inextricably connected, sharing a single existence regardless of distance. The study reveals that at this special squeezing strength, every pair of particles in the system reaches a state of maximum possible entanglement. It is as if the entire system is locked into a state of perfect connection. The researchers found that the exact moments when the quantum phase transitions occur correspond precisely to the moments when these particle pairs are most strongly entangled. In this regime, the chaotic dynamical phase vanishes, leaving behind a clean, geometric evolution. The transition is no longer a messy struggle of forces but a direct manifestation of the system's underlying entangled structure.

The work establishes that by carefully preparing the initial state of a quantum system, scientists can dictate its future behavior with remarkable accuracy. The study demonstrates that double-mode squeezing is not just a theoretical curiosity but a practical protocol for engineering dynamical quantum phases. It bridges the gap between the abstract world of quantum information, where entanglement is a resource, and the physical world of non-equilibrium dynamics, where sudden transitions occur. By showing that maximum entanglement leads to universal, predictable transitions, the researchers provide a new framework for understanding how quantum systems behave far from equilibrium. This insight could be crucial for the development of future quantum technologies, offering a way to design systems that respond to disturbances in a controlled and predictable manner, turning the inherent complexity of quantum mechanics into a manageable feature rather than a barrier.

Technical Summary: Tailoring Dynamical Quantum Phase Transitions via Double-Mode Squeezing Manipulation

Problem Statement
While the squeezing operator is a fundamental tool in quantum metrology and equilibrium many-body physics, its potential for controlling far-from-equilibrium dynamics remains largely unexplored. Specifically, there is a lack of protocols to actively engineer Dynamical Quantum Phase Transitions (DQPTs). Unlike equilibrium phase transitions governed by ground-state properties, DQPTs manifest as nonanalyticities in the Loschmidt echo following a sudden quantum quench. Current research has primarily focused on observing DQPTs under fixed conditions rather than actively inducing, suppressing, or tailoring their occurrence and characteristics. A significant challenge lies in defining a physically realizable squeezing operator that yields genuine state control, as simple constructions in spin-operator space often result only in trivial global phases.

Methodology
The authors investigate a one-dimensional spin-1/2 XY chain in a transverse field, a paradigmatic model for quantum criticality. The study employs a specific protocol involving three stages:

Initialization: The system is prepared in the ground state of a pre-quench Hamiltonian $H_0$ .
Squeezing Manipulation: A double-mode squeezing operator $\hat{S}(\xi)$ $\hat{S} (ξ)$ is applied to the initial state. Crucially, this operator is defined directly in the diagonal Bogoliubov basis $(k, -k)$ $(k, - k)$ of the pre-quench Hamiltonian, rather than in the spin basis. The operator is parameterized by a complex squeezing parameter $\xi = r e^{i\phi}$ $ξ = r e^{i ϕ}$ , where $r$ $r$ is the strength and $\phi$ $ϕ$ is the direction.
- The authors demonstrate that in the spin representation, this operator corresponds to a nonlocal string operator, confirming its nontrivial action.
- The action of the operator is analyzed based on its behavior under Particle-Hole Symmetry (PHS). The operator preserves PHS only if the squeezing parameter is real ( $\phi = 0$ or $\pi$ ).
Quench Dynamics: At $t=0$ , the system parameters are abruptly changed to a post-quench Hamiltonian $\tilde{H}$ . The subsequent time evolution is analyzed via the Loschmidt amplitude $G_s(t) = \langle \psi_s | e^{-i\tilde{H}t} | \psi_s \rangle$ .

The analysis focuses on the Loschmidt rate function $\lambda(t)$ , whose nonanalytic peaks signal DQPTs. These peaks correspond to the intersection of Fisher zeros (zeros of the Loschmidt amplitude in the complex time plane) with the real-time axis. The study also examines the Dynamical Topological Order Parameter (DTOP) derived from the Pancharatnam geometric phase and the intermode entanglement entropy in $(k, -k)$ pairs.

Key Results
The study reveals two distinct regimes of control depending on whether the squeezing operator preserves or breaks PHS:

PHS-Broken Regime (Tunable Control):
- When the squeezing direction $\phi$ breaks PHS, the critical times of DQPTs become highly tunable.
- By varying the squeezing strength $r$ , the intersection points of Fisher zeros with the real-time axis shift continuously.
- This allows for the induction of DQPTs in quenches that would otherwise remain within a single phase (where no transition occurs) and the suppression of DQPTs in quenches that would normally cross a critical point.
PHS-Preserved Regime (Universal Criticality):
- A remarkable universal regime emerges when PHS is preserved ( $\phi = 0$ ) and the squeezing strength reaches a critical value $r = \pi/4$ .
- Fisher Zero Collapse: At this specific point, all Fisher zeros collapse onto the real-time axis, forming a continuous line segment. This leads to a universal class of DQPTs that occurs regardless of the quench path (whether crossing the critical point or staying within a phase).
- Geometric Evolution: At $r = \pi/4$ , the dynamical phase of the Loschmidt amplitude vanishes identically ( $|A_k|^2 = |B_k|^2$ ). Consequently, the time evolution becomes purely geometric, characterized by sharp $\pi$ -jumps in the Pancharatnam geometric phase.
- Entanglement Saturation: The condition for this universal behavior ( $r = \pi/4, \phi = 0$ ) coincides exactly with the condition where the von Neumann entropy of each $(k, -k)$ mode pair reaches its maximum value ( $\ln 2$ ). The critical momenta governing the DQPTs are identical to the modes attaining maximal entanglement.

Significance and Claims
The paper establishes initial-state double-mode squeezing as a versatile protocol for tailoring far-from-equilibrium criticality. The authors claim that their work:

Provides a feasible method to actively engineer DQPTs, moving beyond passive observation to active control (inducing or suppressing transitions).
Reveals a direct link between entanglement saturation and universal nonanalytic dynamics. The emergence of universal DQPTs is shown to be intrinsically tied to the formation of maximally entangled initial states in the Bogoliubov basis.
Demonstrates that squeezing can route a system into a regime where topological signatures (DTOP) emerge from purely geometric evolution, distinct from conventional quenches where dynamical and geometric phases are intertwined.
Offers a conceptual framework for bridging quantum information (double-mode entanglement) with nonequilibrium critical phenomena, suggesting new avenues for engineering dynamical quantum phases in synthetic quantum simulators.

Technical Summary: Tailoring Dynamical Quantum Phase Transitions via Double-Mode Squeezing Manipulation

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