Quantum Simulations With Continuous Variables

Furthering efforts to answer hard-to-test questions about the quantum world, a NIST ion-trap computer can now simulate how the unique rules of quantum mechanics can affect a microscopic particle's "continuous variables," quantities such as position and momentum which can have a smooth continuum of values. Acting as a form of quantum computer, the NIST ion trap might only need a couple of seconds to simulate a quantum physics experiment that can take days to carry out. Moreover, the ion trap can simulate experiments that require rare commodities, like entangled photons, which are created relatively infrequently.

Since quantum computers embrace the unusual logic of the microscopic world, they can perform powerful simulations of its often counterintuitive phenomena. First envisioned by Richard Feynman, quantum simulators are perhaps the earliest practical application of quantum computing--in fact, they have been around for several years now. However, previous versions (Update 438) have only re-created quantum phenomena involving "discrete variables," such as an electron's energy in an atom, which can only have certain prescribed values. The new version recreates quantum processes involving both discrete and continuous variables.

To construct their simulator, NIST researchers in Colorado trap a single beryllium-9 ion with electric fields. As the ion vibrates in the trap, its position and momentum are continuous. This allows the researchers to easily simulate any other complementary pair of continuous variables-such as an electric field's amplitude and phase-which have the exact same mathematical interrelationship. To perform simulations, the researchers shine a series of carefully engineered light pulses on the ion. The pulses cause the ion to act like something it's not, such as an electron bound by an atom, or even a photon as it hits a beamsplitter. Under the influence of the pulses, the ion's quantum states evolve in a way identical to the situation the researchers want to study.

For now, the researchers have performed simple, proof-of-principle demonstrations. As an example, they have investigated how a photon would behave if entangled with other photons by sending it through a beamsplitter. Shining light pulses on the ion to simulate the effects of a beamsplitter on a photon, the researchers have demonstrated that interferometry with up to three other entangled photons would be three times as precise as interferometers using single photons, in line with the recent experimental results on bi-photon interferometry (Update 613). (Leibfried et al., Physical Review Letters, 9 December 2002; Dietrich Leibfried, 303-497-7880, dil@boulder.nist.gov)