Interferometric Qubit Measurement

—University of Washington Quantum System Engineering Group—

This page shows a simulation of a "thought experiment" that investigates a notional method for the interferometric measurement of a two-state quantum system, or qubit.

In this simulated experiment, the qubit is the spin of a trapped ion, a spin-1/2 particle. The state of such a qubit is always a superposition of two basis states: "up" and "down", where each basis state is weighted by a complex amplitude. The polarization (incompletely) summarizes the state in a single real number: +1 for pure spin up, -1 for pure spin down, and intermediate numbers for other states. The animation and the graph depict the polarization as a function of time through the course of one simulated experiment run.

In this simulated experiment, the spin is detected, and also affected, by illuminating it with a beam of light: a stream of photons from a laser photodiode. Each photon interacts with the spin probabilistically. The spin may impart some phase shift to the photon, and the photon may change the state of the spin. The magnitude of the phase shift theta indicates the strength of this interaction. It is usual to describe this effect by the relaxation time constant T1, where a shorter time constant indicates a stronger interaction. The optical fibers and couplers are adjusted such that after the interaction, the photon is detected by a detector photodiode either at the A-channel or B-channel, depending on its phase shift. The time series of detector events constitutes the data of the simulated experiment. In a typical experiment, individual photon detections are not recorded; instead, the instruments behave as a low-pass filter whose output (displayed on an oscilloscope, for example) is similar to the proportion of photons at A calculated by this simulation. (This simulation uses far fewer photons and a much shorter time constant than a typical experiment.)

The state of the spin depends on its initial state and the probabilistic outcomes of the many photon interactions. Whatever the history, however, only two final outcomes are possible: the qubit always settles into a state with polarization -1 or +1. The purpose of this simulation (and the underlying theory) is to show how this result always emerges from any possible initial state and sequence of individual photon interactions. The simulation illustrates how this system exhibits a key phenomenon in quantum physics: measurement results in "collapse" to a basis state.

Repeating the simulation run results in different final outcomes, spin up or down, depending on the (different) initial states and (different, probabilistic) photon interaction outcomes. The final state in each run can be inferred from the time series of detector events: if more photons are detected at A the final spin is up, otherwise the final spin is down. However, the spin state and polarization during their approach to the final state cannot be observed or inferred; it is not possible to identify a specific moment when the state collapses. The time course of the polarization calculated in this simulation is just one of many possible histories that are consistent with the observed detector data.

Details of the experiment and its analysis are explained in the references and expressed in the python code and the time series data it generates. The thought experiment is motivated by Magnetic Resonance Force Microscopy (MRFM), where a microscopic cantilever (which can be modeled as a spin with a very large spin number) replaces the qubit.

References

J. A. Sidles, The AC Stark, Stern-Gerlach, and quantum Zeno effects in interferometric qubit readout, http://arxiv.org/abs/quant-ph/9612001.

John A Sidles et al 2009 New J. Phys. 11 Practical recipes for the model order reduction, dynamical simulation and compressive sampling of large-scale open quantum systems http://www.iop.org/EJ/abstract/1367-2630/11/6/065002

Supported by the Army Research Office (ARO) Multi-University Research Initiative (MURI) W911NF-05-1-0403, and a gift from Microsoft. Design and animation by Neolography.com