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arXiv:1406.1436 · Nature Communications

Exploring the quantum critical behaviour in a driven Tavis–Cummings circuit

Mang Feng, Youpeng Zhong, T. Liu, L.-L. Yan, Wan Li Yang, Jason Twamley, H. Wang

Published May 14, 2015• 55 citations
arXivHTMLPDF

Abstract

Quantum phase transitions play an important role in many-body systems and have been a research focus in conventional condensed-matter physics over the past few decades. Artificial atoms, such as superconducting qubits that can be individually manipulated, provide a new paradigm of realising and exploring quantum phase transitions by engineering an on-chip quantum simulator. Here we demonstrate experimentally the quantum critical behaviour in a highly controllable superconducting circuit, consisting of four qubits coupled to a common resonator mode. By off-resonantly driving the system to renormalize the critical spin-field coupling strength, we have observed a four-qubit nonequilibrium quantum phase transition in a dynamical manner; that is, we sweep the critical coupling strength over time and monitor the four-qubit scaled moments for a signature of a structural change of the system's eigenstates. Our observation of the nonequilibrium quantum phase transition, which is in good agreement with the driven Tavis-Cummings theory under decoherence, offers new experimental approaches towards exploring quantum phase transition-related science, such as scaling behaviours, parity breaking and long-range quantum correlations.

DOI
10.1038/ncomms8111

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Quantum phase transitions play an important role in many-body systems and have been a research focus in conventional condensed-matter physics over the past few decades. Artificial atoms, such as superconducting qubits that can be individually manipulated, provide a new paradigm of realising and exploring quantum phase transitions by engineering an on-chip quantum simulator. Here we demonstrate experimentally the quantum critical behaviour in a highly controllable superconducting circuit, consisting of four qubits coupled to a common resonator mode. By off-resonantly driving the system to renormalize the critical spin-field coupling strength, we have observed a four-qubit nonequilibrium quantum phase transition in a dynamical manner; that is, we sweep the critical coupling strength over time and monitor the four-qubit scaled moments for a signature of a structural change of the system's eigenstates. Our observation of the nonequilibrium quantum phase transition, which is in good agreement with the driven Tavis-Cummings theory under decoherence, offers new experimental approaches towards exploring quantum phase transition-related science, such as scaling behaviours, parity breaking and long-range quantum correlations.
Quantum phase transitions (QPTs) describe when a many-body quantum system displays non-analytic behavior associated with a discontinuous change in a property of the ground state as a parameter is varied. The QPT in prototypical Dicke model is difficult to reach experimentally as the spin–field coupling strength must be quite large. In this work we describe a new model—the off-resonant Tavis–Cummings model where we drive the common mode, and discover a new type of QPT at quite low coupling strengths which are comparable with the geometric mean of the atomic and field detunings . Through analytic methods we demonstrate this QPT for both finite and infinite numbers of spins and show that |〈 J x ( J z )〉|/( N /2) ∼ | λ / λ c − 1| γ x ( γ z ) and 〈 a † a 〉/ N ∼ | λ / λ c − 1| γ a for λ ⩾ λ c , with critical exponents γ x ≈ 1/2, γ z ≈ 1 and γ a ≈ 1. We show that this QPT can be immediately observed by laboratory cavity-QED setups such as Bose–Einstein condensate in optical cavity and superconducting circuit-QED as well as a line of trapped ultracold ions.
Abstract Quantum phase transition (QPT) in the Dicke model has long attracted considerable interest due to its fundamental importance in quantum optics and many-body physics. Recent studies indicate that QPT-like behavior may also arise in the driven Tavis-Cummings (TC) model—a simplified variant of the Dicke model that neglects counter-rotating-wave coupling terms. Hybrid quantum systems, capitalizing on the advantages of different components, offer a promising platform to realize such many-body systems. Here, we experimentally observe a dissipative phase transition in the thermodynamic limit using a driven TC model, implemented by coupling an electron spin ensemble to a superconducting microwave resonator. This QPT behavior is detected via the measurements of Rabi splitting, which exhibits a unique dependence on the collective spin excitations of the system. Our findings provide a route to experimentally investigate critical phenomena in realistic many-body systems under decoherence, and promise potential applications in quantum simulation and other emerging quantum technologies.
The study of phase transitions and critical phenomena arising in quantum driven-dissipative systems, and whether a correspondence can be drawn to their equilibrium counterparts, is a pressing question in contemporary physics. The development of large-scale superconducting circuits provides an experimental platform for these theoretical models. We report an experimental study of a multimode dissipative first-order phase transition in a 1D Bose-Hubbard chain consisting of 21 superconducting resonators. This phase transition manifests itself as a simultaneous frequency jump in all resonator modes as the frequency or power of a pump tone is swept. By measuring the system’s emission spectrum through the transition, we characterize the dim-to-bright phase transition and construct the full phase diagram. We further perform time-dependent measurements of the switching between the two phases in the transition region, from which we corroborate the transition line and extract transition times ranging from a few ms up to 143 s. Our model, based on single-mode mean-field theory and cross-Kerr interactions, captures the features at moderate pump powers and quantitatively reproduces the transition line. Our results open a new window into nonequilibrium quantum many-body physics and mark a step toward realizing and understanding dissipative phase transitions in the thermodynamic limit using superconducting quantum circuits. In addition, our study opens new possibilities for sensing and cryo-switching applications.
Quantum phase transition in Ξ\XiΞ-configuration Tavis-Cummings model driven by an electromagnetic field for a finite number of atoms
The quantum phase transitions of a three-level Tavis-Cummings model in the \Xi Ξ -configuration driven by a single-mode electromagnetic field in a QED cavity are studied for n_a=1,\,2 n a = 1 , 2 , and 4 4 atoms. Although conventional observables like photon number and energy level populations suffice to locate quantum phase transitions, they often lack sensitivity to finite-size effects. Here, we show that the expectation values of the quadratic Casimir invariants associated with the atomic subsystems offer a more robust measure, exhibiting sharp signatures of criticality that are validated by fidelity calculations. Additionally, the von Neumann entropy is employed to map the entanglement landscape between matter and the quantized field. A key finding is that the external driving field acts as a control parameter that shrinks the normal phase region; as the driving intensity increases, the separable ground state vanishes, leading to the dominance of field-matter entanglement across the parameter space.
The Tavis-Cummings model is intensively investigated in quantum optics and has important applications in generation of multi-atom entanglement. Here, we employ a superconducting circuit quantum electrodynamic system to study a modified Tavis-Cummings model with directly-coupled atoms. In our device, three superconducting artificial atoms are arranged in a chain with direct coupling through fixed capacitors and strongly coupled to a transmission line resonator. By performing transmission spectrum measurements, we observe different anticrossing structures when one or two qubits are resonantly coupled to the resonator. In the case of the two-qubit Tavis-Cummings model without qubit-qubit interaction, we observe two dips at the resonance point of the anticrossing. The splitting of these dips is determined by Δ λ =2 g 1 2 + g 3 2 , where g 1 and g 3 are the coupling strengths between Qubit 1 and the resonator, and Qubit 3 and the resonator, respectively. The direct coupling J 12 between the two qubits results in three dressed states in the two-qubit Tavis-Cummings model at the frequency resonance point, leading to three dips in the transmission spectrum. In this case, the distance between the two farthest and asymmetrical dips, arising from the energy level splitting, is larger than in the previous case. The frequency interval between these two dips is determined by the difference in eigenvalues (Δ λ = ε 1+ − ε 1− ), obtained through numerical calculations. What we believe as novel and intriguing experimental results may potentially advance quantum optics experiments, providing valuable insights for future research.
Critical slowing down of the time it takes a system to reach equilibrium is a key signature of bistability in dissipative first-order phase transitions. Understanding and characterizing this process can shed light on the underlying many-body dynamics that occur close to such a transition. Here, we explore the rich quantum activation dynamics and the appearance of critical slowing down in an engineered superconducting quantum circuit. Specifically, we investigate the intermediate bistable regime of the generalized Jaynes-Cummings Hamiltonian (GJC), realized by a circuit quantum electrodynamics (cQED) system consisting of a transmon qubit coupled to a microwave cavity. We find a previously unidentified regime of quantum activation in which the critical slowing down reaches saturation and, by comparing our experimental results with a range of models, we shed light on the fundamental role played by the qubit in this regime.