Squeezed ions in two places at once

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by Tracy Northup from Nature 521, 295–296 (21 May 2015) doi:10.1038/521295a


Experiments on a trapped calcium ion have again exposed the strange nature of quantum phenomena, and could pave the way for sensitive techniques to explore the boundary between the quantum and classical worlds.
In Schrödinger’s famous thought experiment, a cat is prepared in a quantum superposition of being both alive and dead by being trapped in a box with a flask of poison. As if that were not enough, the poor cat is now being squeezed too — all in the name of quantum measurement. In laboratory experiments, atoms have been prepared in superpositions of being in two places at once, playfully called Schrödinger’s cat states(1). Lo et al.(2) demonstrate superposition states of a trapped ion in which its position is not only split between two locations, but also squeezed. Squeezing refers to the process of suppressing quantum fluctuations for a particular measurement, such as that of a particle’s position.
Quantum mechanics tells us that the position of a particle (or Schrödinger’s fictitious cat) has an inherent uncertainty even when it is at rest, a feature known as the standard quantum limit. When the particle is prepared in a squeezed state, however, we can pinpoint its position to better than that limit (Fig. 1). There is a price to pay for squeezing, though. When fluctuations in position are squashed down, additional fluctuations arise in the particle’s momentum, such that the product of position and momentum fluctuations still satisfies Heisenberg’s uncertainty relation — which states that there is a fundamental limit to the precision with which a particle’s position and momentum can be simultaneously determined. Nevertheless, by suppressing fluctuations in the quantity that they intend to measure, researchers can improve measurement precision. For example, squeezed states have been used to achieve record sensitivities for one of the detectors at the Laser Interferometer Gravitational-Wave Observatory in Richland, Washington(3).

Every object's momentum and position are subject to fluctuations, which become pronounced on the atomic scale. a, The red circle indicates the uncertainty in position and momentum for a calcium ion (Ca+) in its motional ground state. b, Lo et al.(2) used laser pulses to squeeze fluctuations in position, at the cost of amplifying the fluctuations in momentum. c, They then displaced the ion in opposite directions at once, so that it would be equally likely to be found in one of two distinct states. The squeezing operation provides a better signal-to-noise ratio for the ion's position, so that it is easier to distinguish between the states.

Every object’s momentum and position are subject to fluctuations, which become pronounced on the atomic scale. a, The red circle indicates the uncertainty in position and momentum for a calcium ion (Ca+) in its motional ground state. b, Lo et al.(2) used laser pulses to squeeze fluctuations in position, at the cost of amplifying the fluctuations in momentum. c, They then displaced the ion in opposite directions at once, so that it would be equally likely to be found in one of two distinct states. The squeezing operation provides a better signal-to-noise ratio for the ion’s position, so that it is easier to distinguish between the states.

The starting point for Lo and colleagues’ study is a single calcium ion (Ca+) trapped by radiofrequency electromagnetic fields in a vacuum vessel. One can picture the trapped ion as a tiny pendulum oscillating around its equilibrium position. For a quantum pendulum in its lowest energy state, the uncertainties in its position and momentum have equal magnitude. In this case, squeezing corresponds to suppressing position fluctuations at the cost of momentum, or vice versa.
The authors use a set of methods known as laser cooling to bring the ion to its motional ground state(4), and then introduce additional laser fields to squeeze the state, reducing the positional variance by a factor of nine. Although squeezed states of trapped ions were first demonstrated 19 years ago(5), the fidelity with which these delicate states are prepared is highly sensitive to experimental noise, such as fluctuating electric and magnetic fields. The authors used a technique called reservoir engineering, which was previously developed by the same research group(6), to achieve robust, high-fidelity squeezing even in the presence of noise.
With the ion in a squeezed ground state, the next step is to prepare it in a cat-state superposition. Imagine that the ion pendulum is displaced by pulling it to one side, then releasing it; it will swing back and forth with the amplitude that has been imparted. Now imagine pulling the ion to the right and left at the same time: classically this does not make sense, but quantum mechanically it is possible.
The way to do this with a trapped ion is to apply a state-dependent force — a displacement whose direction depends on the spin state of the ion’s outermost electron. When the electron is prepared in a superposition of two spin states, the force acts in an equal and opposite direction on each component. As a result, the ion pendulum’s motion is a superposition of two possible oscillations, each with the same amplitude but in opposite directions. In fact, each motional direction is entangled with the electron’s spin state; that is, one property cannot be described independently of the other.
How distinguishable are the two cat-state components from each other? It depends on whether the initial squeezing was performed on the ion’s position or on its momentum. Lo and colleagues measured and compared the two cases. If momentum fluctuations were suppressed before the cat state was prepared, then the corresponding enhancement in position fluctuations made the spatial separation more difficult to distinguish. By contrast, if the ion’s position was squeezed, then the spatial separation between the components became 56 times larger than the extent of the squeezed positional fluctuations.
It is exactly this amplified sensitivity to spatial separation that makes squeezed states promising for future applications. For example, using cat states, the wave nature of a single ion can be exploited for interferometry. In an interferometer, a wave is split, sent along two paths and finally recombined, providing information about how the paths differ. In a cat state, the ion’s location is split into two superposition components, each of which explores a different path. Thus, if the cat-state components are recombined, the superposition acts as an interferometer, probing path differences. Moreover, an ion is highly sensitive to changes in electric and magnetic fields, which shift its electron energy levels, so an ion interferometer could measure field gradients on the scale of tens of nanometres(7). Squeezed cat states would also be more robust than non-squeezed states to certain types of noise, providing improved sensing capabilities.
Building on established techniques for the precise manipulation of trapped ions, the authors have demonstrated an exciting new capability for both engineering and characterizing quantum states. These states are fascinating, not only as future sensors, but also as a means of exploring the boundary between the quantum and classical worlds. The ion pendulum demonstrated by Lo and colleagues has a position uncertainty of only a few nanometres, but it swings back and forth — in two directions at once — over hundreds of nanometres, a much larger distance than atomic scales. Efforts are under way in many research groups to extend cat-state length scales even further, into truly macroscopic regimes.
Future work with squeezed cat states will continue to characterize their strange, often counter-intuitive, quantum properties. Here, as the authors have shown, single ions provide an exceptional experimental platform on which to do so.


(1) Monroe, C., Meekhof, D. M., King, B. E. & Wineland, D. J. Science 272, 1131–1136 (1996).
(2) Lo, H.-Y. et al. Nature 521, 336–339 (2015).
(3) Aasi, J. et al. Nature Photon. 7, 613–619 (2013).
(4) Leibfried, D., Blatt, R., Monroe, C. & Wineland, D. Rev. Mod. Phys. 75, 281–324 (2003).
(5) Meekhof, D. M., Monroe, C., King, B. E., Itano, W. M. & Wineland, D. J. Phys. Rev. Lett. 76, 1796–1799 (1996).
(6) Kienzler, D. et al. Science 347, 53–56 (2015).
(7) Poyatos, J. F., Cirac, J. I., Blatt, R. & Zoller, P. Phys. Rev. A 54, 1532–1540 (1996).

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