Session M11: Focus Session: Measurement Induced Phase Transitions and Quantum Simulation of Phase Transitions

Measurement induced phase transition in ground states

An external observer can have a profound impact on the quantum state that it is observing. Recent studies of random quantum circuits have shown that if the object of observation is a large many-body system, then mere observation can induce a phase transition in the large scale quantum correlations of the system. In this talk I will argue that observing a quantum ground state can similarly lead to a phase transition in the structure of long range correlations in the state. As a concrete example I will consider the impact of weak measurement of the density of a one dimensional quantum liquid applied for a finite time.   

Observing a purification phase transition with a trapped ion quantum computer

Many-body open quantum systems balance internal dynamics against decoherence from interactions with an environment. Here, we explore this balance via random quantum circuits implemented on a trapped-ion quantum computer, where the system evolution is represented by unitary gates with interspersed projective measurements. As the measurement rate is varied, a purification phase transition is predicted to emerge at a critical point akin to a fault-tolerent threshold. We probe the "pure'' phase, where the system is rapidly projected to a deterministic state conditioned on the measurement outcomes, and the "mixed'' or "coding'' phase, where the initial state becomes partially encoded into a quantum error correcting codespace.  We find evidence of the two phases and show numerically that, with modest system scaling, critical properties of the transition emerge.   

Experimental Realization of Rabi-Hubbard Model with Trapped Ions

Quantum simulation provides important tools in studying strongly correlated many-body systems with controllable parameters. As a hybrid of two fundamental models in quantum optics and in condensed matter physics, Rabi-Hubbard model demonstrates rich physics through the competition between local spin-boson interactions and long-range boson hopping. Here we report an experimental realization of the Rabi-Hubbard model using up to 16 trapped ions and present a controlled study of its equilibrium properties and quantum dynamics. We observe the ground-state quantum phase transition by slowly quenching the coupling strength, and measure the quantum dynamical evolution in various parameter regimes. With the magnetization and the spin-spin correlation as probes, we verify the prediction of the model Hamiltonian by comparing theoretical results in small system sizes with experimental observations. For larger-size systems of 16 ions and 16 phonon modes, the effective Hilbert space dimension exceedss 2⁵⁷, whose dynamics is intractable for classical supercomputers.   

Non-equilibrium critical phenomena in a trapped-ion quantum simulator

Recent work has predicted that quenched near-integrable systems can exhibit dynamics associated with thermal, quantum, or purely non-equilibrium phase transitions, depending on the initial state [1]. Using a trapped-ion quantum simulator with intrinsic long-range interactions, we investigate collective non-equilibrium properties of critical fluctuations after quantum quenches. In particular, we probe the scaling behavior of fluctuations near the critical point of the ground-state disorder-to-order phase transition, after single and double quenches of the transverse field in a long-range Ising Hamiltonian. With system sizes of up to 50 ions, we show that both the post-quench fluctuation magnitude and dynamics scale with system size with distinct critical exponents, charaterizing the type of phase-transition. Furthermore we demonstrate that the critical exponents after a single and a double quenches are different and correspond to effectively thermal and truly non-equilibrium behavior, respectively. Our results demonstrate the ability of quantum simulators to explore universal scaling beyond the equilibrium context. 

 [1] Paraj Titum and Mohammad F. Maghrebi, Phys. Rev. Lett. 125, 040602 (2020).   

Landau-Forbidden Quantum Criticality in Rydberg Atom Arrays

A continuous transition between two distinct symmetry broken phases is generally forbidden to occur within the celebrated Landau-Ginzburg-Wilson theory of phase transitions. However, a quantum effect can intertwine the two symmetries, giving rise to a novel scenario called deconfined quantum criticality. In this work, we propose a model of a one-dimensional array of strongly-interacting, individually trapped neutral atoms interacting via Rydberg states, and demonstrate through extensive numerical simulations that its ground state phase diagram exhibits deconfined quantum criticality in certain parameter regimes. Moreover, we show how an enlarged, emergent continuous symmetry arises at these critical points, which can be directly observed via studying the joint distribution of two competing order parameters in the natural measurement basis. Our findings highlight quantum simulators of Rydberg atoms not only as natural platforms to experimentally realize such exotic phenomena, but also as unique ones as they allow access to physical properties not accessible in traditional condensed matter experiments.   

Diagnosing dynamical phase transitions in Spin-1 Bose-Einstein condensate using classical and quantum information

Non-equilibrium dynamics has been used to probe quantum many-body physics and to perform state engineering which finds broad applications in various aspects of quantum technologies. Dynamical phase transitions (DPT), which signal different dynamical structures of a quantum system by tuning control parameters, provides a powerful tool to classify many-body dynamics in closed quantum systems. In this work, we identify an order parameter to diagnose the DPT in quench dynamics of a Spin-1 Bose-Einstein condensate for classical initial states (coherent spin states) which is motivated by a mean-field picture of the double-well structure in the phase space. Beyond the classical regime, a quantum probe based on the quantum Fisher information (QFI) is shown to be able to capture such a DPT for a broader type of initial states including both coherent spin states and Fock states. The classical Fisher information (CFI), as is more realistic to be measured in Spin-1 Bose-Einstein condensate nowadays, is also shown to mimic the role of QFI to some degrees and is useful in diagnosing such a DPT. Both the CFI and the QFI make a smooth connection between DPTs and quantum sensing.