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Physical Review A

Experimental demonstration of decoherence-induced spontaneous symmetry breaking

Yun‐Feng Huang, Liang Peng, Li Li, Bi‐Heng Liu, Chuan‐Feng Li, Guang‐Can Guo

Published May 3, 2011• 1 citation
Publisher

Abstract

We experimentally investigate the variations of exchange-symmetry properties of the four Bell states in an exchange-symmetric pure dephasing process with a two-photon system generated from spontaneous parametric down-conversion (SPDC). Experiment results show that under such an exchange-symmetric local-noise Hamiltonian, the exchange-symmetry property remains unchanged for two of the three symmetric Bell states, i.e., the states $|\ensuremath{\Phi}\ensuremath{\rangle}{}^{\ifmmode\pm\else\textpm\fi{}}=\frac{1}{\sqrt{2}}(|00\ensuremath{\rangle}\ifmmode\pm\else\textpm\fi{}|11\ensuremath{\rangle})$. For the antisymmetric Bell state $|\ensuremath{\Psi}\ensuremath{\rangle}{}^{\ensuremath{-}}=\frac{1}{\sqrt{2}}(|01\ensuremath{\rangle}\ensuremath{-}|10\ensuremath{\rangle})$, the exchange-symmetry property increases and achieves a maximum value of 0.5 at the asymptotic limit. However, for the third exchange-symmetric Bell state $|\ensuremath{\Psi}\ensuremath{\rangle}{}^{+}=\frac{1}{\sqrt{2}}(|01\ensuremath{\rangle}+|10\ensuremath{\rangle})$, the exchange-symmetry property breaks, surviving with a probability of 0.5 at the asymptotic limit, which provides some evidence supporting such decoherence-induced spontaneous-symmetry-breaking phenomena.

DOI
10.1103/physreva.83.052105

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We experimentally investigate the variations of exchange-symmetry properties of the four Bell states in an exchange-symmetric pure dephasing process with a two-photon system generated from spontaneous parametric down-conversion (SPDC). Experiment results show that under such an exchange-symmetric local-noise Hamiltonian, the exchange-symmetry property remains unchanged for two of the three symmetric Bell states, i.e., the states ∣\ensuremathΦ\ensuremath⟩\ifmmode±\else\textpm\fi=12(∣00\ensuremath⟩\ifmmode±\else\textpm\fi∣11\ensuremath⟩)|\ensuremath{\Phi}\ensuremath{\rangle}{}^{\ifmmode\pm\else\textpm\fi{}}=\frac{1}{\sqrt{2}}(|00\ensuremath{\rangle}\ifmmode\pm\else\textpm\fi{}|11\ensuremath{\rangle})∣\ensuremathΦ\ensuremath⟩\ifmmode±\else\textpm\fi=2​1​(∣00\ensuremath⟩\ifmmode±\else\textpm\fi∣11\ensuremath⟩). For the antisymmetric Bell state ∣\ensuremathΨ\ensuremath⟩\ensuremath−=12(∣01\ensuremath⟩\ensuremath−∣10\ensuremath⟩)|\ensuremath{\Psi}\ensuremath{\rangle}{}^{\ensuremath{-}}=\frac{1}{\sqrt{2}}(|01\ensuremath{\rangle}\ensuremath{-}|10\ensuremath{\rangle})∣\ensuremathΨ\ensuremath⟩\ensuremath−=2​1​(∣01\ensuremath⟩\ensuremath−∣10\ensuremath⟩), the exchange-symmetry property increases and achieves a maximum value of 0.5 at the asymptotic limit. However, for the third exchange-symmetric Bell state ∣\ensuremathΨ\ensuremath⟩+=12(∣01\ensuremath⟩+∣10\ensuremath⟩)|\ensuremath{\Psi}\ensuremath{\rangle}{}^{+}=\frac{1}{\sqrt{2}}(|01\ensuremath{\rangle}+|10\ensuremath{\rangle})∣\ensuremathΨ\ensuremath⟩+=2​1​(∣01\ensuremath⟩+∣10\ensuremath⟩), the exchange-symmetry property breaks, surviving with a probability of 0.5 at the asymptotic limit, which provides some evidence supporting such decoherence-induced spontaneous-symmetry-breaking phenomena.
Spontaneous symmetry breaking (SSB) is crucial to the occurrence of phase transitions. Once a phase transition occurs, a quantum system presents degenerate eigenstates that lack the symmetry of the Hamiltonian. After crossing the critical point, the system is essentially evolved to a quantum superposition of these eigenstates until decoherence sets in. Despite the fundamental importance and potential applications in quantum technologies, such quantum-mechanical SSB phenomena have not been experimentally explored in many-body systems. We here present an experimental demonstration of the SSB process in the Lipkin-Meshkov-Glick model, governed by the competition between the individual driving and intraqubit interaction. The model is realized in a circuit quantum electrodynamics system, where 6 Xmon qubits are coupled in an all-to-all manner through virtual photon exchange mediated by a resonator. The observed nonclassical correlations among these qubits in the symmetry-breaking region go beyond the conventional description of SSB, shedding new light on phase transitions for quantum many-body systems.
One of the most intriguing features of entanglement is that entangled quantum systems exhibit exchange symmetry; that is, local quantum operations on the subsystems may be interchanged without affecting the quantum state. In this work, we investigate whether the exchange symmetry is preserved for the weak (or partial collapse) measurement, a type of quantum operation, in the presence of decoherence. Demonstrated using two entangled photonic polarization qubits, the experimental results clearly show that the exchange symmetry is broken once decoherence is introduced, even though the photons still share nonzero entanglement. Our results shed light on quantum state manipulation using general quantum operations on entangled quantum states in the presence of decoherence.
Simultaneous entanglement in spin and space-time of a two-photon quantum state generated in type-2 spontaneous parametric down-conversion is demonstrated by the observation of quantum interference with 98% visibility in a simple beam-splitter (Hanburry Brown-Twiss) anticorrelation experiment. The nonlocal cancellation of two-photon probability amplitudes as a result of this double entanglement allows us to demonstrate two different types of Bell's inequality violations in one experimental setup.
Solids appear to have localised centres of mass, yet many-body quantum theory describes them using translationally symmetric models that preclude localisation. Conventionally, this is resolved through spontaneous symmetry breaking by introducing an interaction with a semiclassical environment that breaks the symmetry. In the thermodynamic limit, the interaction can be removed while leaving the state localised. This, however, raises the question of how localisation arises outside the thermodynamic limit, i.e., in finite quantum systems (Wallace, 2018). Here, we show that, by quantising the environment, the localisation of finite systems occurs within decoherent branches, while the state vector of the composite system remains translationally symmetric. Our approach is analogous to the Page-Wootters construction (Page & Wootters, 1983) and quantum reference frames; moreover, we recover the semiclassical description as a limiting case while predicting experimentally distinguishable corrections away from this limit.
Symmetry in mixed quantum states can manifest in two distinct forms: , where each individual pure state in the quantum ensemble is symmetric with the same charge, and , which applies only to the entire ensemble. This paper explores a novel type of spontaneous symmetry breaking (SSB) where a strong symmetry is broken to a weak one. While the SSB of a weak symmetry is measured by the long-ranged two-point correlation function, the strong-to-weak SSB (SWSSB) is measured by the . We prove that SWSSB is a universal property of mixed-state quantum phases, in the sense that the phenomenon of SWSSB is robust against symmetric low-depth local quantum channels. We also show that the symmetry breaking is “spontaneous” in the sense that the effect of a local symmetry-breaking measurement cannot be recovered locally. We argue that a thermal state at a nonzero temperature in the canonical ensemble (with fixed symmetry charge) should have spontaneously broken strong symmetry. Additionally, we study nonthermal scenarios where decoherence induces SWSSB, leading to phase transitions described by classical statistical models with bond randomness. In particular, the SWSSB transition of a decohered Ising model can be viewed as the “ungauged” version of the celebrated toric-code decodability transition. We confirm that, in the decohered Ising model, the SWSSB transition defined by the fidelity correlator is the only physical transition in terms of channel recoverability. We also comment on other (inequivalent) definitions of SWSSB, through correlation functions with higher Rényi indices.