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Entanglement with Frequency Combs

February 24, 2010

For the first time, scientists have employed a powerful technique of laser physics – the “optical frequency comb” – to entangle two trapped atoms.* This form of control is a promising candidate for use as a logic gate for quantum computing and information-processing, and offers substantial operational advantages over other methods of laser-generated entanglement.

The team, led by JQI Fellow Christopher Monroe, began by preparing two ytterbium ions, spaced about five micrometers apart in an electrical trap, in identical minimal-energy ground states. [See Figure 1] The goal of the experiment was to entangle these two ions – that is, to place them in a condition in which the quantum state of one is inextricably connected to the state of the other – using light from a single high-speed pulsed laser.

Entanglement is the method that will likely be used for transferring quantum information from place to place in any future quantum computer or information-processing system. As a result, there is intense global interest in finding dependable, high-speed entanglement schemes.

The researchers entangled the ions in a two-part process in which both parts occur simultaneously, generated by the laser pulses. In part one, the ions are placed in a superposition of two hyperfine states – tiny energy differences within a single excitation level of an atom that result from electrons’ interaction with the nucleus. The hyperfine states serve as a two-level system that permits each ion to function as a quantum information bit, or “qubit,” as it exists in some combination of both states at the same time.

In part two, the laser pulses give each ion a momentum “kick” that depends on which qubit state it is in. These kicks are slight physical displacements that cause each positively charged ion to affect the other through interaction of their electrical fields. There are multiple pathways by which a sequence of photons can place each ion in a given quantum vibrational state. Owing to a peculiarity of quantum mechanics, when it is impossible to know which photon sequence put the ions in their target vibrational states, the ions are entangled. [See Figure 2]

“These sorts of procedures have been done before with continuous-wave lasers,” says Dave Hayes, first author on the paper, “but never with a frequency comb.”

An optical frequency comb is a peculiar property of pulsed, “mode-locked” lasers. In the cavity of a laser, photons with a narrow range of frequencies reflect back and forth between the two mirrors on either end. [See Figure 3] Many of those frequencies will be suppressed by destructive interference; they cancel themselves out because the round-trip distance from mirror to mirror in the cavity is not an integer multiple of their wavelengths. But many frequencies will have exactly the right wavelengths to resonate in the cavity, forming standing waves like a jump rope. Each of those standing waves is a mode of the cavity.

When all the modes have the same phase relationship to each other, they are said to be “mode-locked,” and something remarkable happens: At periodic intervals, the standing waves interfere constructively – that is, reinforce each other – forming a very brief, intense pulse with a duration in the picosecond range or even shorter. (A picosecond is one millionth of one millionth of a second.) The JQI team used a train of 1-picosecond pulses separated by 12.5 nanoseconds.

Each pulse consists of multiple frequencies, which over time build up into a pattern of sharply defined frequency spikes that are uniformly spaced like the teeth in a comb. If the energy difference between any two comb frequencies corresponds exactly with an atomic quantum transition, it will produce it. But many desired effects – including those sought by the JQI team – do not precisely match any spacing in the teeth of a single comb. So the scientists split the main pulsed laser beam into separate beams and applied slight frequency offsets to them with devices called acousto-optic modulators (AOMs).

By tuning the system with the AOMs, the team can create any frequency difference they want to produce both the target effects: generating qubit states in the ions, and entangling the ions by momentum kicks. For the latter, Hayes says, “when we can use two teeth from offset combs to match the energy of transition between motion quanta, we’re in business to entangle neighboring ions.”

“There are inherent advantages of the frequency comb method,” Hayes notes. “One consideration is cost. Mode-locked lasers are just cheaper, especially for ions because the transitions are usually in the ultraviolet. Continuous-wave lasers in that frequency range are really expensive, while it’s simple to generate uv light with these high power pulses.” The main criterion governing the type of pulsed laser to be used is the bandwidth – the range of frequencies that can be carried in the pulses.

The JQI researchers used a titanium-doped sapphire laser for this experiment. “What’s special about the beam,” Hayes says, “is that the bandwidth of a single pulse is larger than the energy difference between the two qubit states.”

The comb method is also attractive because of the potential for much higher laser powers, delivered in a much shorter time span, which could allow quantum logic gates to operate very fast. While this aspect was not part of this demonstration, it will be addressed in future experiments. But more generally, as Hayes explains, “the optical frequency comb has so many frequency markers that this system should also be useful for the quantum control of almost any optical quantum system, from other atomic species to molecules or even quantum dots.”

* See reference publication.