Heisenberg Uncertainty Principle as Probe of Entanglement Entropy: Application to Superradiant Quantum Phase Transitions

Abstract

Quantum phase transitions are often embodied by the critical behavior of purely quantum quantities such as entanglement or quantum fluctuations. In critical regions, we underline a general scaling relation between the entanglement entropy and one of the most fundamental and simplest measure of the quantum fluctuations, the Heisenberg uncertainty principle. Then, we show that the latter represents a sensitive probe of superradiant quantum phase transitions in standard models of photons such as the Dicke Hamiltonian, which embodies an ensemble of two-level systems interacting with one quadrature of a single and uniform bosonic field. We derive exact results in the thermodynamic limit and for a finite number N of two-level systems: as a reminiscence of the entanglement properties between light and the two-level systems, the product $\Delta x\Delta p$ diverges at the quantum critical point as $N^{1/6}$. We generalize our results to the double quadrature Dicke model where the two quadratures of the bosonic field are now coupled to two independent sets of two level systems. Our findings, which show that the entanglement properties between light and matter can be accessed through the Heisenberg uncertainty principle, can be tested using Bose-Einstein condensates in optical cavities and circuit quantum electrodynamics

arXiv comment7 pages, 3 figures. Published Version

References in corpus (53)

• A computable measure of entanglement
• Circuit Quantum Electrodynamics: Coherent Coupling of a Single Photon to a Cooper Pair Box
• Cavity quantum electrodynamics for superconducting electrical circuits: an architecture for quantum computation
• Entanglement in quantum critical phenomena
• Scaling of Entanglement close to a Quantum Phase Transitions
• Manipulating the Quantum State of an Electrical Circuit
• The Dicke Quantum Phase Transition with a Superfluid Gas in an Optical Cavity
• Entanglement in a simple quantum phase transition
• Ground state overlap and quantum phase transitions
• Chaos and the Quantum Phase Transition in the Dicke Model
• Quantum vacuum properties of the intersubband cavity polariton field
• Extremal entanglement and mixedness in continuous variable systems
• Preparation and Measurement of Three-Qubit Entanglement in a Superconducting Circuit
• Measurement-Induced Entanglement for Excitation Stored in Remote Atomic Ensembles
• Proposed realization of the Dicke-model quantum phase transition in an optical cavity QED system
• Quantum Chaos Triggered by Precursors of a Quantum Phase Transition: The Dicke Model
• Deep Strong Coupling Regime of the Jaynes-Cummings model
• Entanglement and the Phase Transition in Single Mode Superradiance
• Generation of Three-Qubit Entangled States using Superconducting Phase Qubits
• Exploring Symmetry Breaking at the Dicke Quantum Phase Transition
• Measuring entanglement growth in quench dynamics of bosons in an optical lattice
• The Dicke model phase transition in the quantum motion of a Bose-Einstein condensate in an optical cavity
• Quantum Noise as an Entanglement Meter
• Qubit-oscillator systems in the ultrastrong-coupling regime and their potential for preparing nonclassical states
• Heralded Entanglement between Atomic Ensembles: Preparation, Decoherence, and Scaling
• Is there a no-go theorem for superradiant quantum phase transitions in cavity and circuit QED ?
• Bipartite Fluctuations as a Probe of Many-Body Entanglement
• Finite-Size Scaling Exponents of the Lipkin-Meshkov-Glick Model
• Continuous unitary transformations and finite-size scaling exponents in the Lipkin-Meshkov-Glick model
• Measuring entanglement entropy of a generic many-body system with a quantum switch
• Entanglement scaling in critical two-dimensional fermionic and bosonic systems
• Equivalence of critical scaling laws for many-body entanglement in the Lipkin-Meshkov-Glick model
• Estimating entanglement measures in experiments
• Finite-Size Scaling Exponents in the Dicke Model
• Entanglement Entropy, decoherence, and quantum phase transition of a dissipative two-level system
• Vacuum degeneracy of a circuit-QED system in the ultrastrong coupling regime
• Protected quantum computation with multiple resonators in ultrastrong coupling circuit QED
• Entanglement and Entropy in a Spin-Boson Quantum Phase Transition
• Universal geometric entanglement close to quantum phase transitions
• Entanglement Entropy beyond the Free Case
• Entanglement and Criticality in Quantum Impurity Systems
• Entanglement Entropy of the Two-Dimensional Heisenberg Antiferromagnet
• Detecting Quantum Critical Points using Bipartite Fluctuations
• Universality of the negativity in the Lipkin-Meshkov-Glick model
• Circuit QED with a Nonlinear Resonator : ac-Stark Shift and Dephasing
• Benchmarking a Teleportation Protocol realized in Superconducting Circuits
• Measuring entanglement in condensed matter systems
• Towards measuring Entanglement Entropies in Many Body Systems
• Multipartite entanglement detection via structure factors
• Quantum phase transitions in fully connected spin models: an entanglement perspective
• Strong tunable coupling between a superconducting charge and phase qubit
• Delocalized Entanglement of Atoms in optical Lattices
• Double symmetry breaking and 2D quantum phase diagram in spin-boson systems

Cited by in corpus (18)

• Superradiance transition in a system with a single qubit and a single oscillator
• Quantum Fisher information as signature of superradiant quantum phase transition
• Many-Body Quantum Electrodynamics Networks: Non-Equilibrium Condensed Matter Physics with Light
• Scaling of genuine multiparticle entanglement at a quantum phase transition
• Dicke coupling by feasible local measurements at the superradiant quantum phase transition
• The quantum entropic uncertainty relation and entanglement witness in the two-atom system coupling with the non-Markovian environments
• Driven dissipative dynamics and topology of quantum impurity systems
• Fluctuations and Entanglement spectrum in quantum Hall states
• Scaling of entanglement entropy across Lifshitz transitions
• Bipartite charge fluctuations in one-dimensional ${\mathbb{Z}}_2$ superconductors and insulators
• Bipartite Fluctuations and Topology of Dirac and Weyl Systems
• Field-dependent superradiant quantum phase transition of molecular magnets in microwave cavities
• Quantum phase transitions in the triangular coupled-top model
• Quantum Phase Transitions in a Generalized Dicke Model
• The reduction of entropy uncertainty for qutrit system under non-Markov noisy environment
• Circuit-based cavity magnonics in the ultrastrong and deep-strong coupling regimes
• The dynamics of entropy uncertainty for qutrit system under the random telegraph noise
• Universal Uncertainty Principle in Different Quantum Theories