Ideally, measurement of the energy state of a single atom would set the atom to the measured state without affecting any of its other properties. This goal has now been achieved with the assistance of a small optical cavity. See Letter p.210
In classical physics, a measurement can in principle be carried out with unlimited precision without affecting the system being measured. In quantum physics, by contrast, every measurement that reveals information about a quantum system necessarily exerts a back-action on the system; this effect is also known as the collapse of the wavefunction. However, most measurements performed in the laboratory lead to a much larger back-action than is imposed by quantum theory.
On page 210 of this issue, Volz et al.1 describe how an optical cavity can allow a single atom to be measured with essentially only the back-action required by quantum theory. Their result not only deepens our understanding of the boundary between quantum and classical physics, but is also a step towards making atom-based quantum-information processing a reality2.
Consider a single atom with two long-lived energy states. The atom can be either in one of these energy states or — and this is a property unique to quantum theory — in both states simultaneously. In an ideal 'von Neumann' measurement3,4 of the energy state, the atom will be found in one of the two energy states. Furthermore, the measurement back-action will set the atom to the measured state. Any subsequent measurement of the energy state will yield the same result. Besides setting the atom to the measured state, no further back-action is mandated by quantum theory. Although it should be possible to measure the energy state of the atom with no additional back-action involved in the process, and thus without energy exchange between the atom and the measurement probe, such an ideal measurement has not been achieved. Volz and colleagues' study1 offers the means to do just this.
Previously, state-of-the-art measurements of the energy state of single trapped atoms were performed by fluorescence detection5,6. In this method, light is shone on the atom to excite it from one of its two ground states — say, the 'bright' state — into a third state, whereupon it spontaneously emits a photon and returns to the original state (Fig. 1a). With this closed optical-transition system, an atom in the bright state will absorb and emit (scatter) many photons. An atom in the other state, the 'dark' state, is not excited by the incident light and remains dark. Collecting and detecting the scattered photons allows the quantum state of the atom to be determined with high fidelity7. However, the large number of scattered photons can heat the atom, and might leave it in a state other than its two ground states. Theoretical investigations8 also show that detecting the state of an atom using a single-pass laser beam is always accompanied by spontaneous scattering of photons.
To overcome these limitations, Volz and colleagues1 used a small optical cavity, an arrangement of two highly reflective mirrors that allows light to bounce back and forth between them (Fig. 1b,c). If a multiple of the half-wavelength of the laser light impinging on the cavity matches the distance between the mirrors, the cavity becomes nearly transparent to the light. By contrast, if this condition is not met, most light is reflected. The authors' microscopic cavity, which was made of highly reflective coated optical fibres, can reflect a photon more than 40,000 times on average before it is lost. This microscopic cavity with its high-reflectivity mirrors enabled the authors to reach a regime in which even a single atom can strongly shift the wavelength at which light resonates in the cavity.
In this set-up, an atom in the bright state, with an optical transition that is resonant with the cavity, shifts the cavity's resonance frequency, and most of the incoming light is reflected (Fig. 1c). In the dark state, the atom does not 'see' the light and consequently does not change the resonance frequency of the cavity, which remains transparent to the incident light (Fig. 1b). What's more, in both states the atom scatters hardly any photons. By separately detecting photons reflected from and transmitted through the cavity, the authors could measure the quantum state of the atom9 without energy exchange being incurred. Volz and colleagues1 determined the state of a single atom with more than 90% fidelity and with spontaneous scattering of less than 0.2 photons on average — therefore, the atom is subjected to almost no heating.
The knowledge about the atom's quantum state that the experiment can reveal is limited by the quantum efficiency of the instruments used to detect the light. Nevertheless, by means of a feature known as the quantum Zeno effect10, the authors were able to quantify the back-action exerted on the atom and thereby determine the average time between measurements. The atom is first prepared in one of the two ground states, for example in the bright state. Before the state is measured, an incident microwave pulse induces transitions between the two ground states. After the pulse, the atom is always found in the other state — the dark state, in this example. If the state of the atom is measured after a much shorter time than the duration of the pulse, there is a high probability of finding the atom in the original state: in this case, the measurement back-action resets the atom to the original state. Decreasing the time between several state measurements strongly increases the probability of finding the atom in the original state. As a consequence, the atom can be frozen in the initial quantum state by measuring it very often — this is the quantum Zeno effect.
Volz and colleagues employ this effect to determine the frequency with which the atomic state is reset, and thus the frequency with which measurements of the atomic state are performed. They show that an average of two photons incident on the cavity is sufficient for a measurement of the internal state of the atom, setting the atomic state to either the bright or dark state. This result quantifies the measurement back-action and demonstrates the potential of cavity-assisted state detection of single atoms.
Volz and co-workers' experiment1 furthers our understanding of the quantum-measurement process and the interactions between a quantum system and its environment. It can be used to execute fast quantum-state measurements of atoms that deliver a result for each atom. The ability to make such measurements is essential for fundamental tests of quantum mechanics11. Measurement of the quantum state without heating while simultaneously allowing preparation of the atom in one of the states is also an important tool for creating a neutral-atom-based quantum computer2.
The fidelity of quantum-state detection and the spontaneous photon-scattering rate achieved in the current experiment are still limited by technical imperfections in the cavity1. An improved cavity, or one embedded in an interferometer12, would open the path to quantum-state detection of trapped molecules without the need to use closed optical transitions13.
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