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Quantum speed up in an optical cavity

July 27, 2015

Control systems are ubiquitous, and as essential as they are easy to overlook. For instance, turning the dial on a thermostat feels as trivial as moving a piece on a board game, but this control system is actually quite complex. Electricity is used to continuously compress a gas outside the home, so that the air will cool as it re-expands until the molecules inside are moving as slow as the user specified. The goal is an equilibrium state: once the temperature settles, the heat is pumping out as fast as it leaks in. Humans seem to have a particular knack for, or maybe even an obsession with, engineering systems that act on exceptionally complex dynamics in order to reach arbitrarily specified  "set-points".

Take, for example, Cavity Quantum ElectroDynamics (CQED) research, which at its heart is a high-finesse optical cavity. An optical cavity is a construct familiar to anyone who has spent time between aisles of a shoe store or in an over-mirrored elevator. Fundamentally, it is an arrangement of mirrors with the property that an object within it can see its reflection multiple times. In the elevator, there may be a dozen visible reflections; an atom in the optical cavity used here will "see" itself twenty thousand times. In CQED experiments, researchers use this effect to confine photons, or particles of light, and study their interaction with matter. In particular, physicists are interested in controlling the dynamics of the photons and bending them to their will to, for example, perform specific tasks as fast as possible. However, the quantum mechanical properties of the photons limit implementing arbitrarily fast controls. This effect has been coined a "quantum speed limit".

The quantum speed limit describes the maximum rate at which a quantum system, here the quantized field of the optical cavity, can transition from one state to another. Now, Luis Orozco’s group at JQI, in collaboration with researchers from Shanxi University, China and Los Alamos National Laboratory have studied how fast a photon trapped inside of a cavity settled as they varied its coupling to a reservoir of laser-cooled atoms. The results were published recently in the journal Physical Review Letters, and show that the atomic environment could provide a speed-up in the time it took for the system to reach equilibrium.

The basic principle behind this research can be understood in analogy to accelerating in a car. Pushing the throttle releases fuel into the cylinders and the car speeds up until the energy produced by burning the fuel is balanced by the energy lost to drag during every combustion cycle. This is ‘steady-state’ for the engine, and it can be reached faster by adding more fuel -- pushing the throttle harder.  Similarly, steady-state behavior for the optical cavity occurs when light escapes as fast as it enters, i.e., when balanced loss and gain is achieved. However, the team works on the scale of individual photons, and, in this limit, the steady state is reached when a single photon trapped in the cavity finally escapes. While it is trapped in the cavity, the photon bounces between the mirrors and may be absorbed by atoms and can be re-emitted into the cavity many times before it eventually travels through the mirror instead of reflecting.

The acceleration of a car depends on the rate of fuel burning. This can be thought of as increasing the coupling between a source of energy (the fuel) and a reservoir to disperse it in (kinetic energy of the car, and its drag). Making the car lighter and more aerodynamic can increase this coupling, as well as just pouring in more gas. In the experiment, the researchers take the latter approach. Laser-cooled atoms are randomly distributed through the volume of the cavity, and can be treated as a reservoir in contact with the electric field produced by the trapped photon. For the experimental parameters used here, the only way the team could increase the coupling between the photon and the atomic environment was to take a page from 1960's hot-rod engineers and crank up the rubidium atom dispenser. 

As they varied this coupling, the researchers discovered that something unusual happened as the atom-photon system evolved in time. To understand what they saw, consider that vast majority of controllable systems are characterized as ‘Markovian,’ which means they do not show any sign of “memory”. The future state of the system is determined only by its current state, and is completely independent of its past. For instance, the future temperature of a house depends only on the thermostat setting and its current temperature, but has nothing to do with how hot or cold it was last week. In the car analogy, the future speed of your car depends only on how fast you are going and how hard you push the throttle, but not the number of yellow lights you have sped through or the time you have idled through traffic.

In a system with memory, i.e., a non-Markovian system, past states of a system can interact with its present state, and determine its future. In this experimental setup, an atom in the cavity interacts with thousands of mirror-images of itself on the scale of nanoseconds. This property significantly enhances the rate-of-evolution from an excited state into equilibrium. Specifically, when a photon becomes trapped in the cavity it couples with the atoms and all of its own time-delayed mirror images. Each emission and re-absorption scrambles the photons phase in a random way, and increases the chance of its escape. Analogously, this is like a car accelerating faster from a stop because it was rear ended by a past version of itself.

In complex systems, the strategy for achieving robust functionality is to accumulate as many independent control parameters as possible. The automobile is nineteenth-century technology, but by using advanced sensing and control systems, Google’s self-driving car managed to drive itself cross-country to tour Washington, D.C. While certainly very different, quantum systems like this one are as messy as they are complex, and successful control relies on being able to understand and tune it in as many ways as possible. The new “knob” these researchers found gives them fast control over the system’s evolution, and accumulating more may allow them to build quantum systems that autonomously navigate through Hilbert space like Google’s car does the streets of the nation's capital.

This article was written by JQI graduate student B. Patterson.