Measuring geometric phases with a dynamical quantum Zeno effect in a Bose-Einstein condensate

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 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

Interplay between geometric and dynamic phases in a single-spin system

“…An intriguing direction of further investigation is exploiting the quantum Zeno effect [49], where repeated projective measurements on one state of the two-level system during a cyclic state manipulation yields a phase that cancels the φ dyn accumulated during a C pulse. Recently demonstrated for a two-level spin system formed from a 87 Rb Bose-Einstein condensate [50], the quantum Zeno scheme yields a measured phase consistent with the purely geometric AA phase. Our work presents an ideal opportunity to further evaluate the Zeno scheme and reveal purely geometric quantum-state evolution.…”

Inhibiting phase drift in multi-atom clocks using the quantum Zeno effect

“…It can be seen that the Zeno effect can inhibit the growth of the superradiant states and maintain a fixed relative phase within each of the states k E and k G as before. The probability of success drops off at the same rates as shown in Figure 5 if we choose 1  and 2  equal to the parameter  in equation (15).…”

“…In the quantum Zeno effect [11][12][13] , frequent measurements can inhibit transitions into unwanted states and force the system to evolve in the desired subspace of Hilbert space. The Zeno effect has been experimentally demonstrated using 9 Be + ground-state hyperfine levels 14 , Bose-Einstein condensates 15 , ion traps 16 , nuclear magnetic resonance 17 , cold atoms 18 , cavity QED 19 , and large atomic systems 13 . It has also been shown that the Zeno effect is a sufficient resource for the implementation of quantum logic gates 20,21 , which could be used as the basis of a quantum computer 21 or quantum repeaters 22 .…”

Quantum Zeno effects across a parity-time symmetry breaking transition in atomic momentum space

“…The decay of an unstable quantum system can be suppressed by frequent projective measurements, whose back actions repeatedly interrupt the time evolution of the system. Such a phenomenon, famed as the quantum Zeno effect, has been experimentally observed in various physical systems [1][2][3][4][5], and has found widespread utilities in quantum information [6][7][8][9][10][11][12][13][14][15][16] and quantum simulation [17][18][19][20][21]. In a complementary fashion, with an appropriate repetition rate of measurements, the decay of the system can also be enhanced under what is known as the anti-Zeno effect [22].…”