The Anyon Zeno Effect

Abstract

Two anyons encircling each other acquire a quantized braiding phase that is independent of their spatial separation. We show that detecting this phase in a fractional quantum Hall interference experiment results in a quantum Zeno effect: a localized anyon is trapped by constant observation from a stream of anyons supplied by the measurement current. Interferometers with an embedded antidot are ideal for accessing the Zeno regime, where the bare tunneling rate of localized anyons is much lower than the measurement rate. The Zeno-suppressed tunneling rate of the trapped anyon depends on the braiding phase and the transmission of the quantum point contacts. Our primary prediction is that the autocorrelation time of the conductance through the interferometer increases with the bias current. This effect may be used to experimentally control the anyon dynamics, in particular to increase the lifetime of localized anyons.

Figures (4)

• Figure 1: Fabry-Pérot Interferometer (a) and Optical Mach-Zehnder Interferometer (b) with embedded quantum antidots. The localized anyon 'Bob' (green) can tunnel between states $|1\rangle$ in the center and $|0\rangle$ outside the loop. His tunneling is disrupted by the interfering anyon 'Alice' (purple), propagating from the source $S$ to the drains $D1$, $D2$, along edge states with the indicated chirality.
• Figure 2: (a) A tunneling sequence of Alice and Bob at QPC1 that can be viewed as time-domain braiding Han2016. This process interlinks their worldlines and is associated with a phase $e^{2 i \theta}$. (b)-(d) Three mechanisms determine Bob's dynamics: Continuous Hamiltonian time evolution, unitary kicks due to Alice's passage and measurements that partially project Bob onto the states $|0\rangle$ or $|1\rangle$.
• Figure 3: (a) and (b) Simulated time evolution of the conductance through an OMZI whose bulk realizes the $\nu=\frac{1}{3}$ Laughlin state with $50\%$ transmission at both QPCs. The magnitudes of the jumps depend on the Aharonov-Bohm flux $\Phi_\mathrm{AB}$. (c) Conductance histogram as a function of $\Phi_\mathrm{AB}$. Orange and blue markers indicate the values chosen for the time traces. (d) The autocorrelation functions $C(\Delta t)$ for independent simulations with the same parameters as in (a) or (b). They exhibit an identical exponential decay before reaching the noise floor due to finite sampling time.
• Figure 4: (a) The anyon lifetime depends only weakly on the braiding phase $\theta$. No data are shown for very small $\theta$, where $C(\Delta t)$ no longer follows an exponential decay. (b) The dependence of Bob's lifetime on the QPC transmission follows Eq. \ref{['eqn.life']}. Variations of 10% in the measurement rate lead to slight deviations in the limit of a nearly closed QPC. (c) Crossover between the Zeno and anti-Zeno regimes as a function of the measurement rate. All data include error bars reflecting the small variations between independent simulations that differ in the measurement outcomes.