Observation of parity-time symmetry breaking in a single-spin system

Abstract

A fundamental axiom of quantum mechanics requires the Hamiltonians to be Hermitian which guarantees real eigen-energies and probability conservation. However, a class of non-Hermitian Hamiltonians with Parity-Time (PT ) symmetry can still display entirely real spectra [1]. The Hermiticity requirement may be replaced by PT symmetry to develop an alternative formulation of quantum mechanics [2, 3]. A series of experiments have been carried out with classical systems including optics [4], electronics [5][6][7], microwaves[8], mechanics [9] and acoustics [10][11][12]. However, there are few experiments to investigate PT symmetric physics in quantum systems. Here we report the first observation of the PT symmetry breaking in a single spin system. We have developed a novel method to dilate a general PT symmetric Hamiltonian into a Hermitian one, which can be realized in a practical quantum system. Then the state evolutions under PT symmetric Hamiltonians, which range from PT symmetric unbroken to broken regions, have been experimentally observed with a single nitrogen-vacancy (NV) center in diamond. Due to the universality of the dilation method, our result opens a door for further exploiting and understanding the physical properties of PT symmetric Hamiltonian in quantum systems. arXiv:1812.05226v1 [quant-ph]

Quantum Sensing with a Single-Qubit Pseudo-Hermitian System

“…The above non-Hermitian Hamiltonian cannot be directly realized in a closed quantum system [52,59]. In order to achieve an effective pseudo-Hermitian quantum arXiv:1910.06553v1 [quant-ph] 15 Oct 2019 system satisfying the following Schrödinger equation…”

“…we adopt a Naimark dilation approach [20,22,52] using an extended Hermitian system. The evolution of the total system (including the system s and the ancilla qubit a) |Ψ(t) = |0 a ⊗ |ψ(t) s + |1 a ⊗ |χ(t) s follows a dilated Hamiltonian H [58].…”

“…Analysis of sensing performance.-The experimental realization of a pseudo-Hermitian qubit sensor relies on the conditional evolution in a dilated Hermitian quantum system [20,22,52]. This approach results in a finite success probability γ(λ o , τ ) (7.4 − 10.4 √ ε)ε 2 [58], which equals to the probability of the ancilla qubit in the state |0 a , see Fig.1.…”

“…Nevertheless, the singular behavior of the energy splitting is counteracted by the eigenstate coalescence [46][47][48]. Quantum sensing based on non-Hermitian qubit system without involving exceptional points and its potential advantages remain largely unexplored.In this work, we propose a novel strategy to harness a qubit probe with pseudo-Hermiticity as a resource for quantum sensing by introducing an additional qubit ancilla [49][50][51][52]. The dilated two-qubit Hermitian system, when exposed to a parameter-dependent weak field, reproduces an effective pseudo-Hermitian qubit sensor by postselection, inheriting the influence of the parameter.…”

Effective non-Hermitian physics for degenerate ground states of a non-Hermitian Ising model with $\mathcal{RT}$ symmetry

“…Since Paritytime (PT )-symmetric non-Hermitian quantum theory was put forward by Bender and Boettcher [1][2][3] in the 1990s, it attracts massive researches in different fields in recent years. Many platforms were proposed to realize PT -symmetric non-Hermitian symmetric quantum mechanics, such as optical systems [4][5][6][7], electronics [8][9][10], microwaves [11], acoustics [12][13][14] and single-spin system [15]. Some applications associated with PTsymmetric system have been explored including unidirectional transport [16,17] and single-mode lasers [18,19].…”