Squeezing Quantum Phase Transition
Oklahoma State University (OSU) physicists have discovered a universal “Squeezing Phase Transition,” which creates new dynamical phases of matter and increases the basic knowledge of how entanglement is produced in intricate quantum systems. A team comprising postdoctoral researcher Samuel Begg, assistant professor Dr. Thomas Bilitewski, and graduate student Arman Duha examined this phenomenon.
Nonequilibrium Dynamics and Entanglement Generation
Power-law interacting spin-1/2 bilayer XXZ models are used to study nonequilibrium dynamics of quantum spins interacting over extended distances. For quantum metrology, creating entangled states is essential, especially through techniques like spin squeezing, which tries to lower quantum noise below the conventional quantum limit in order to facilitate quantum-enhanced sensing.
The two layers are polarised in opposite directions in a straightforward, readily generated initial state from which the dynamics are started. Two-mode squeezing results from the dynamic creation of entangled pairs of excitations by the interlayer spin-exchange interactions. Importantly, the system moves out of equilibrium, which means that new nonequilibrium phases of matter are classified by their universal features.
Two Distinct Dynamical Phases
The OSU group discovered a dramatic change between two different dynamical regimes, which they categorized as phases of matter because of their shared characteristics:
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- The Fully Collective Phase
Heisenberg-limited scaling, the highest theoretical maximum for quantum-enhanced sensing, is reached by the system in this phase. Dr. Bilitewski compared the fully collective regime to a swarm of fireflies synchronizing their flashes, where all the spins synchronize and operate collectively.
The behavior of the squeezed observable’s minimal variance in relation to the system size is the primary feature that characterizes this phase. The minimal variance scales with an exponent of zero in the fully collective phase, meaning it is independent of the system size. To maximize the accuracy of quantum sensors, this collective behavior is ideal.
- The Partially Collective Phase
On the other hand, scalable squeezing is a feature of the partially collective phase. The system nevertheless permits quantum-enhanced sensing, which gets better with system scale, even though the spins in this regime do not function entirely collectively.
For a particular two-dimensional example, the variance was found to scale with a positive exponent linked to the system size. In this phase, the minimal variance is more than a constant number and scales positively with the system size. Even in the face of intense local interactions that could otherwise push the intricate, many-body system towards chaos, this regime shows that quantum information persists.
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Nature of the Phase Transition
A new dynamical phase transition occurs when these two regimes change from the completely collective to the partially collective phase. These regimes are established as separate dynamical phases within the framework of non-equilibrium critical events since this change takes place in the system’s time development rather than as a typical equilibrium phase transition (such as ice melting).
The system’s physical properties, specifically the aspect ratio (the ratio of the layer separation to the layer length scale) and the interaction power-law exponent, determine the transition point itself. There is a crucial value of the aspect ratio for systems with a big power-law exponent in relation to the dimension; the system is completely collective above this critical value and enters the partially collective regime below it.
It was discovered that the dynamics in the partially collective phase obeyed universal principles, which are comparable to those governing systems near well-known equilibrium phase transitions. System parameters and a divergent time scale characterize the scaling of the squeezing dynamics. A scaling ansatz that relates the smallest variance to the system size and aspect ratio captures this universal scaling.
The fact that the critical exponents describing this transition are the same even for various lattice geometries (such as square, triangular, and hexagonal lattices in two dimensions) provides additional support for universality and strongly implies that the phenomena are not influenced by the minute details of the particular system configuration.
Connecting to Excitation Modes
By looking at the excitation spectrum of the system, it is natural to understand the physical genesis of these phases. Only the collective momentum mode (sometimes referred to as the k=0 mode) is unstable in the completely collective phase, and it grows exponentially to produce the required two-mode squeezing entanglement. All other momentum modes stay stable.
Nevertheless, several finite-momentum modes become unstable in the partially collective regime. These modes would rapidly decrease the collective spin length and depolarise the system if they were allowed to grow unchecked. As a result, interactions are necessary to inhibit the creation of these finite momentum excitations, proving that the partially collective phase exists and that basic quadratic theory alone is insufficient to explain this occurrence.
Implications for Quantum Technology
Future quantum technology will be greatly impacted by the identification of the universal Squeezing Phase Transition and its crucial scale. The results significantly advance our knowledge of the reliable generation of entanglement, which is an essential tool for creating quantum systems that have a significant edge over classical ones.
In particular, this study promotes developments in quantum sensing, which uses entanglement to attain previously unheard-of measurement accuracy for uses in fundamental science, medical imaging, and navigation.
These results are also instantly applicable to existing experimental platforms that can realize long-range spin interactions, such as trapped ion arrays and cold-atomic, molecular, or Rydberg systems. These cutting-edge platforms have already shown the necessary mechanisms, like Floquet engineering of interactions. The study answers a key challenge about attaining scalable squeezing beyond conventional paradigms by establishing scalable two-mode squeezing even with power-law interactions.
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