## Breaking symmetry with single spins

The energetics of quantum systems are typically described by Hermitian Hamiltonians. The exploration of non-Hermitian physics in classical parity-time (PT)–symmetric systems has provided fertile theoretical and experimental ground to develop systems exhibiting exotic behavior. Wu *et al.* now demonstrate that non-Hermitian physics can be found in a solid-state quantum system. They developed a protocol, termed dilation, which transformed a PT-symmetric Hamiltonian into a Hermitian one. This allowed them to investigate PT-symmetric physics with a single nitrogen-vacancy center in diamond. The results provide a starting point for exploiting and understanding the exotic properties of PT-symmetric Hamiltonians in quantum systems.

*Science*, this issue p. 878

## Abstract

Steering the evolution of single spin systems is crucial for quantum computing and quantum sensing. The dynamics of quantum systems has been theoretically investigated with parity-time–symmetric Hamiltonians exhibiting exotic properties. Although parity-time symmetry has been explored in classical systems, its observation in a single quantum system remains elusive. We developed a method to dilate a general parity-time–symmetric Hamiltonian into a Hermitian one. The quantum state evolutions ranging from regions of unbroken to broken

In quantum mechanics, the real energies of a system are guaranteed by a fundamental axiom associated with the Hermiticity of physical observables. However, a class of non-Hermitian Hamiltonians satisfying parity-time (*1*). An alternative formulation of quantum mechanics can be established when the axiom of Hermiticity is replaced by the condition of *2*, *3*). The physics associated with *4*, *5*). The optical analog of *6*) and then extended to other systems, such as electronics (*7*–*9*), microwaves (*10*), mechanics (*11*), acoustics (*12*–*14*), and optical systems with atomic media (*15*–*17*). Experimental study on *18*, *19*) and single-mode lasers (*20*, *21*).

Experimentally investigating *22*). Some progress has been made with this approach in the system of light-matter quasiparticles (*23*, *24*). A lossy Hamiltonian has been constructed to simulate the quantum dynamics under *25*). However, the additional dissipation introduced in this protocol is usually detrimental to quantum features such as coherence and entanglement. Instead of engineering *26*, *27*). Alternatively, two theoretical approaches have been developed to dilate a *28*, *29*). However, these dilation methods are limited to the cases of unbroken

For the

The Hamiltonian, *30*)]. For example, *I* is the identity matrix. We note that this derivation of

We investigate the *r* is a real number. The eigenvalues of *E* are real, and the system is in an unbroken-symmetry region. Especially, the Hamiltonian *E* appears, and the system is in a broken-symmetry region. The point

A single nitrogen-vacancy (NV) center in diamond (Fig. 1A) is used to demonstrate our proposal. The Hamiltonian of the NV center is

To realize the

The experiment was performed on an optically detected magnetic resonance setup. The static magnetic field was set to 506 G, and the NV center was polarized into the state *31*). Then the initial state was prepared to

The state evolution under

The

Our work makes NV center a desirable platform for investigating important non-Hermitian physics, such as new topological invariants (*32*–*35*), quantum thermodynamics (*36*), and information criticality (*29*) in this scenario. This platform can be used to investigate various models of decoherence and dissipation in open quantum systems (SM5 and fig. S6). Furthermore, the feature of the exceptional point can be used to improve the sensitivity of quantum sensing (*37*, *38*). This is expected to enhance the performance of NV-based quantum sensor with a variety of applications.

## Supplementary Materials

science.sciencemag.org/content/364/6443/878/suppl/DC1

Materials and Methods

Supplementary Text

Figs. S1 to S6

Table S1

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## References and Notes

**Acknowledgments:**We thank J. Gong for the helpful discussion.

**Funding:**This work was supported by the National Key R&D Program of China (grant nos. 2018YFA0306600 and 2016YFB0501603), the NNSFC (grant no. 11761131011), the Chinese Academy of Sciences (grant nos. GJJSTD20170001, QYZDY-SSW-SLH004, and QYZDB-SSW-SLH005), and Anhui Initiative in Quantum Information Technologies (grant no. AHY050000). X.R. thanks the Youth Innovation Promotion Association of Chinese Academy of Sciences for their support.

**Author contributions:**J.D. and X. R. proposed the idea and supervised the experiments. X.R., J.G., and Y.W. designed the experiments. Y.W. and W.L. performed the experiments. X.Y. prepared the sample. J.G. and X.S. elaborated the theoretical framework. Y.W. and W.L. carried out the calculations. All authors analyzed the data, discussed the results, and wrote the manuscript.

**Competing interests:**The authors declare no competing interests.

**Data and materials availability:**All data are available in the manuscript or the supplementary materials.