In the ideal quantum Zeno (QZ) effect, repeated quantum projective measurements can freeze the coherent dynamics of a quantum system. However, in the weak QZ regime, measurement backactions can allow the sensing of semi-classical field fluctuations. In this regard, we theoretically show how to combine the controlled manipulation of a quantum two-level system, used as a probe, with a sequence of projective measurements to have direct access to the noise correlation function. We experimentally test the effectiveness of the proposed noise sensing method on a properly engineered Bose-Einstein condensate of Rb 87 atoms realized on an atom chip. We believe that our QZ-based approach can open a new path towards novel quantum sensing devices.

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 measurementfree 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.Introduction.-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]. This technique provides a robust method for quantum control of populations, as has been demonstrated experimentally, e.g., for the static quantum Zeno effect with trapped ions [5] and atoms [6], as well as for dynamical evolutions with atoms [7-9]. Interestingly, an evolution driven by quantum back-action may also induce a nontrivial change of the quantum mechanical phase, despite the phase-insensitive nature of projective measurements. Indeed, the evolution along a closed trajectory gives rise to a geometric phase factor, on top of a possible dynamical phase that depends on the realization of the trajectory. A closer inspection reveals that the geometric phase is imprinted by the final projection in the sequence, whereas all previous projections effectively freeze the evolution of the geometric, but not of the dynamical phase.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 now 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]. Controlling and manipulating geometric phase factors provides a robust alternative to engineering quantum states by purely dynamical evolutions. As such, these techniques have potential applications in the field of quantum information, in particular, quantum simulations [19] and quantum computations [20]. Geometric phases that arise in a sequence of projections have first been discussed in the pioneering work of Pancharatnam [21], and were subject of several subsequent studies [22][23][24][25][26].In this work, we experimentally generate and measure geometric phase factors in a Bose-Einstein condensate using a