Abstract
Open physical systems with balanced loss and gain, described by non-Hermitian parity-time left( {{cal P}{cal T}} right) reflection symmetric Hamiltonians, exhibit a transition which could engender modes that exponentially decay or grow with time, and thus spontaneously breaks the {cal P}{cal T}-symmetry. Such {cal P}{cal T}-symmetry-breaking transitions have attracted many interests because of their extraordinary behaviors and functionalities absent in closed systems. Here we report on the observation of {cal P}{cal T}-symmetry-breaking transitions by engineering time-periodic dissipation and coupling, which are realized through state-dependent atom loss in an optical dipole trap of ultracold 6Li atoms. Comparing with a single transition appearing for static dissipation, the time-periodic counterpart undergoes {cal P}{cal T}-symmetry breaking and restoring transitions at vanishingly small dissipation strength in both single and multiphoton transition domains, revealing rich phase structures associated to a Floquet open system. The results enable ultracold atoms to be a versatile tool for studying {cal P}{cal T}-symmetric quantum systems.
Highlights
Open physical systems with balanced loss and gain, described by non-Hermitian parity-time ðPT Þ reflection symmetric Hamiltonians, exhibit a transition which could engender modes that exponentially decay or grow with time, and spontaneously breaks the PT -symmetry
A non-Hermitian parity-time reflection symmetric (PT -symmetric) Hamiltonian, that is invariant under combined parity ðPÞ and time-reversal ðT Þ operations, has been considered as a natural extension of the conventional Hermitian quantum theory to describe an open quantum system with balanced loss and gain[1,2,3]
PT -symmetric Hamiltonians have been realized in balanced gain and loss systems with various setups, such as mechanical oscillators[13], optical waveguides[14,15], optical resonators[16], microwave cavities[17], lasers[18], and optomechanical systems[19], or in a state-dependent pure lossy system in which the lossy Hamiltonian H′ could be mapped to a PT -symmetric Hamiltonian HPT for passive PT -symmetry breaking[20,21,22]
Summary
Open physical systems with balanced loss and gain, described by non-Hermitian parity-time ðPT Þ reflection symmetric Hamiltonians, exhibit a transition which could engender modes that exponentially decay or grow with time, and spontaneously breaks the PT -symmetry. Such PT -symmetry-breaking transitions have attracted many interests because of their extraordinary behaviors and functionalities absent in closed systems. We present an experimental study of PT -symmetrybreaking transitions induced by time-periodic dissipation or coupling in a two-spin system of ultracold atoms. We further map the Floquet PT -phase diagrams by tracing the atom loss of each spin state, and observe the multiphoton resonances and the power broadening associated to the PTSB phase
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