Abstract We present an analytic and numerica study of a class of geometric phase induced by weak measurements. In particular, we analyze the dependence of the geometric phase on the winding W of the polar angle φ, upon a sequence of N weak measurements of increased magnitude (c), resulting in the appearance of a multiplicity of critical measurement-strength parameters where the geometric phase becomes stochastic. Adding to the novelty of our approach, we not only analyze the weak-measurement-induced geometric phase by a full analytic derivation, valid in the quasi-continuous limit (N → ∞), but also we analyze the induced geometric phase numerically, thus enabling us to unravel the finite-N interplay of the geometric phase with the measurement strength parameter, and its stability to perturbations in the measurements protocol.Abstract We present an analytic and numerica study of a class of geometric phase induced by weak measurements. In particular, we analyze the dependence of the geometric phase on the winding W of the polar angle φ, upon a sequence of N weak measurements of increased magnitude (c), resulting in the appearance of a multiplicity of critical measurement-strength parameters where the geometric phase becomes stochastic. Adding to the novelty of our approach, we not only analyze the weak-measurement-induced geometric phase by a full analytic derivation, valid in the quasi-continuous limit (N → ∞), but also we analyze the induced geometric phase numerically, thus enabling us to unravel the finite-N interplay of the geometric phase with the measurement strength parameter, and its stability to perturbations in the measurements protocol.

Jun 26, 20240 citations

Topological weak-measurement-induced geometric phases revisited

Graciana Puentes

We present an analytical and numerical study of a class of geometric phase induced by weak measurements. In particular, we analyze the dependence of the geometric phase on the winding ( $W$ ) of the polar angle ( $φ$ ), upon a sequence of $N$ weak measurements of increased magnitude ( $c$ ), resulting in the appearance of a multiplicity of critical measurement-strength parameters where the geometric phase becomes stochastic. Adding to the novelty of our approach, we not only analyze the weak-measurement induced geometric phase by a full analytic derivation, valid in the quasicontinuous limit ( $N \rightarrow \infty$ ), but also we analyze the induced geometric phase numerically, thus enabling us to unravel the finite- $N$ interplay of the geometric phase with the measurement strength parameter, and its stability to perturbations in the measurements protocol.We present an analytical and numerical study of a class of geometric phase induced by weak measurements. In particular, we analyze the dependence of the geometric phase on the winding ($W$) of the polar angle ($φ$), upon a sequence of $N$ weak measurements of increased magnitude ($c$), resulting in the appearance of a multiplicity of critical measurement-strength parameters where the geometric phase becomes stochastic. Adding to the novelty of our approach, we not only analyze the weak-measurement induced geometric phase by a full analytic derivation, valid in the quasicontinuous limit ($N \rightarrow \infty$), but also we analyze the induced geometric phase numerically, thus enabling us to unravel the finite-$N$ interplay of the geometric phase with the measurement strength parameter, and its stability to perturbations in the measurements protocol.

arXiv:2406.00176May 31, 20240 citations

Weak-measurement-induced phases and dephasing: Broken symmetry of the geometric phase

Kyrylo Snizhko, Nihal Rao, Parveen Kumar +1 more

Coherent steering of a quantum state, induced by a sequence of weak measurements, has become an active area of theoretical and experimental study. For a closed steered trajectory, the underlying phase factors involve both geometrical and dynamical terms. Furthermore, considering the reversal of the order of the measurement sequence, such a phase comprises a symmetric and an antisymmetric term. Superseding common wisdom, we show that the symmetric and the antisymmetric components do not correspond to the dynamical and geometrical parts, respectively. Addressing a broad class of measurement protocols, we further investigate the dependence of the induced phases on the measurement parameters (e.g., the measurement strength). We find transitions between different topologically distinct sectors, defined by integer-valued winding numbers, and show that the transitions are accompanied by diverging dephasing. We propose experimental protocols to observe these effects.Coherent steering of a quantum state, induced by a sequence of weak measurements, has become an active area of theoretical and experimental study. For a closed steered trajectory, the underlying phase factors involve both geometrical and dynamical terms. Furthermore, considering the reversal of the order of the measurement sequence, such a phase comprises a symmetric and an antisymmetric term. Superseding common wisdom, we show that the symmetric and the antisymmetric components do not correspond to the dynamical and geometrical parts, respectively. Addressing a broad class of measurement protocols, we further investigate the dependence of the induced phases on the measurement parameters (e.g., the measurement strength). We find transitions between different topologically distinct sectors, defined by integer-valued winding numbers, and show that the transitions are accompanied by diverging dephasing. We propose experimental protocols to observe these effects.

Jan 1, 202112 citations

Weak-measurement-induced phases and dephasing: Broken symmetry of the geometric phase

Kyrylo Snizhko, Nihal Rao, Parveen Kumar +1 more

arXiv:2006.14641Physical Review ResearchOct 18, 20219 citations

Observing a topological transition in weak-measurement-induced geometric phases

Yunzhao Wang, Kyrylo Snizhko, Alessandro Romito +2 more

Measurement plays a quintessential role in the control of quantum systems. Beyond initialization and readout which pertain to projective measurements, weak measurements, in particular through their back action on the system, may enable various levels of coherent control. The latter ranges from observing quantum trajectories to state dragging and steering. Furthermore, just like the adiabatic evolution of quantum states that is known to induce the Berry phase, sequential weak measurements may lead to path-dependent geometric phases. Here we measure the geometric phases induced by sequences of weak measurements and demonstrate a topological transition in the geometric phase controlled by measurement strength. This connection between weak measurement-induced quantum dynamics and topological transitions reveals subtle topological features in measurement-based manipulation of quantum systems. Our protocol could be implemented for classes of operations (e.g., braiding) that are topological in nature. Furthermore, our results open new horizons for measurement-enabled quantum control of many-body topological states.Measurement plays a quintessential role in the control of quantum systems. Beyond initialization and readout which pertain to projective measurements, weak measurements, in particular through their back action on the system, may enable various levels of coherent control. The latter ranges from observing quantum trajectories to state dragging and steering. Furthermore, just like the adiabatic evolution of quantum states that is known to induce the Berry phase, sequential weak measurements may lead to path-dependent geometric phases. Here we measure the geometric phases induced by sequences of weak measurements and demonstrate a topological transition in the geometric phase controlled by measurement strength. This connection between weak measurement-induced quantum dynamics and topological transitions reveals subtle topological features in measurement-based manipulation of quantum systems. Our protocol could be implemented for classes of operations (e.g., braiding) that are topological in nature. Furthermore, our results open new horizons for measurement-enabled quantum control of many-body topological states.

arXiv:2102.05660Physical Review ResearchJun 3, 202225 citations

Topological transitions of the generalized Pancharatnam-Berry phase

Manuel F. Ferrer-Garcia, Kyrylo Snizhko, Alessio D’Errico +3 more

Distinct from the dynamical phase, in a cyclic evolution, a system's state may acquire an additional component, a.k.a. geometric phase. Recently, it has been demonstrated that geometric phases can be induced by a sequence of generalized measurements implemented on a single qubit. Furthermore, it has been predicted that these geometric phases may exhibit a topological transition as a function of the measurement strength. We demonstrate and study this transition experimentally by using an optical platform where the qubit is represented by the polarization of light and the weak measurement is performed by means of coupling with the spatial degree of freedom. Our protocol can be interpreted in terms of environment-induced geometric phases, whose values are topologically determined by the environment-system coupling strength. Our results show that the two limits of geometric phase induced by sequences of either weak or projective measurements are topologically distinct.Distinct from the dynamical phase, in a cyclic evolution, a system's state may acquire an additional component, a.k.a. geometric phase. Recently, it has been demonstrated that geometric phases can be induced by a sequence of generalized measurements implemented on a single qubit. Furthermore, it has been predicted that these geometric phases may exhibit a topological transition as a function of the measurement strength. We demonstrate and study this transition experimentally by using an optical platform where the qubit is represented by the polarization of light and the weak measurement is performed by means of coupling with the spatial degree of freedom. Our protocol can be interpreted in terms of environment-induced geometric phases, whose values are topologically determined by the environment-system coupling strength. Our results show that the two limits of geometric phase induced by sequences of either weak or projective measurements are topologically distinct.

Science AdvancesNov 24, 202313 citations

We present an analytical and numerical study of a class of geometric phase induced by weak measurements. In particular, we analyze the dependence of the geometric phase on the winding (

W

) of the polar angle (

φ

), upon a sequence of

N

weak measurements of increased magnitude (

c

), resulting in the appearance of a multiplicity of critical measurement-strength parameters where the geometric phase becomes stochastic. Adding to the novelty of our approach, we not only analyze the weak-measurement induced geometric phase by a full analytic derivation, valid in the quasicontinuous limit (

N \rightarrow \infty

), but also we analyze the induced geometric phase numerically, thus enabling us to unravel the finite-

N

interplay of the geometric phase with the measurement strength parameter, and its stability to perturbations in the measurements protocol.