Abstract
A closed-trajectory evolution of a quantum state generally imprints a phase that contains both dynamical and geometrical contributions. While dynamical phases depend on the reference system, geometric phase factors are uniquely defined by the properties of the outlined trajectory. Here, we generate and measure geometric phases in a Bose-Einstein condensate of $^{87}$Rb using a combination of dynamical quantum Zeno effect and measurement-free evolution. We show that the dynamical quantum Zeno effect can inhibit the formation of a geometric phase without altering the dynamical phase. This can be used to extract the geometric Aharonov-Anandan phase from any closed-trajectory evolution without requiring knowledge or control of the Hamiltonian.
Highlights
The dynamical quantum Zeno effect describes an evolution induced by measurement back-action, forcing the system to follow a sequence of projections [1,2,3,4]
While dynamical phases depend on the reference system, geometric phase factors are uniquely defined by the properties of the outlined trajectory
Our analysis reveals that the origin of the geometric phase can be traced back to the Aharonov-Anandan phase that is generated in the final evolution [step (ii)]
Summary
The dynamical quantum Zeno effect describes an evolution induced by measurement back-action, forcing the system to follow a sequence of projections [1,2,3,4]. Geometric phases in quantum physics were first systematically studied for adiabatic evolutions by Berry [10] and later generalized to arbitrary periodic evolutions by Aharonov and Anandan [11]. They are an integral part of all fields of quantum physics [12] and have been observed in several experiments, including nuclear magnetic resonance [13], molecular systems [14], graphene [15], solid-state qubits [16], and cold atoms [17,18]. This leads to a robust method to isolate geometric phase factors from dynamical contributions, even if the Hamiltonian cannot be controlled
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