Two-atom bunching

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by Lindsay J. LeBlanc from Nature 520, 36–37 (02 April 2015) doi:10.1038/520036a


The Hong–Ou–Mandel effect, whereby two identical quantum particles launched into the two input ports of a ‘beam-splitter’ always bunch together in the same output port, has now been demonstrated for helium-4 atoms.
All particles, including photons, electrons and atoms, are described by a characteristic list of ‘quantum numbers’. For a pair of particles whose lists match, there is no way of telling them apart — they are perfectly indistinguishable. One of the more intriguing consequences of quantum mechanics arises from this indistinguishability, and was exemplified(1) in an experiment by Hong, Ou and Mandel (HOM) in the 1980s. The researchers showed that, although a single photon approaching an intersection along one of two input paths exits in one of two output paths with equal probability, identical pairs brought to the intersection simultaneously from different paths always exit together. Lopes et al.(2) now demonstrate this manifestation of two-particle quantum interference for two identically prepared — and thus indistinguishable — helium-4 atoms. The result provides an opportunity to extend advances made in quantum optics to the realm of atomic systems, especially for applications in quantum information.
As a graduate student faced with finding a wedding present for my labmate, I decided that the HOM experiment was a fitting analogy to marriage: from two separate paths, this couple’s lives were intersecting and would continue along a single path together. Along with the formalism describing the effect tucked into the card, I gave them a glass ‘beam-splitter’ to represent a key ingredient in the optical demonstration of the effect: this glass cube could act as the intersection, at which half the light incident on any of the four polished faces is transmitted, with the remaining half being reflected; for single particles, the probabilities for transmission and reflection are both 50%. All HOM experiments require a ’50:50 beam-splitting’ mechanism that sends quantum particles incident along one of two input paths to one of two output paths with a 50% probability (Fig. 1a).

Each beam-splitter (blue) is represented as two input paths (left) and two output paths (right); here we consider '50:50' beam-splitters, for which the probability of each output is of equal magnitude. A particle is represented by a red circle, and its wavefunction's phase by the position of the black dot on the grey circle. Individual phases cannot be measured directly. a, Possible outcomes for a single particle entering either of the input paths; the probabilities for particle transmission and reflection are both 50%. In the case of reflection, the phase changes by 90°. b, For incoming particles at both inputs, there are four possible outcomes. However, the overall probability of the outcomes is determined by adding the individual probabilities using rules of quantum mechanics. For bosonic particles such as photons and helium-4 atoms, the subject of Lopes and colleagues' study(2), the first two outcomes (transmit/transmit and reflect/reflect) cancel. The only outcomes remaining are the third and the fourth.

Each beam-splitter (blue) is represented as two input paths (left) and two output paths (right); here we consider ’50:50′ beam-splitters, for which the probability of each output is of equal magnitude. A particle is represented by a red circle, and its wavefunction’s phase by the position of the black dot on the grey circle. Individual phases cannot be measured directly. a, Possible outcomes for a single particle entering either of the input paths; the probabilities for particle transmission and reflection are both 50%. In the case of reflection, the phase changes by 90°. b, For incoming particles at both inputs, there are four possible outcomes. However, the overall probability of the outcomes is determined by adding the individual probabilities using rules of quantum mechanics. For bosonic particles such as photons and helium-4 atoms, the subject of Lopes and colleagues’ study(2), the first two outcomes (transmit/transmit and reflect/reflect) cancel. The only outcomes remaining are the third and the fourth.

Careful analysis shows that there must be a well-defined relationship between the beam-splitter’s inputs and outputs that is demanded by energy conservation in the classical picture of the beam-splitter3, or by a property known as unitarity in the quantum view4: for classical waves, this relationship fixes the relative positions of the output waves’ peaks and valleys with respect to those of the input waves, whereas for quantum particles this relationship manifests as a relative ‘phase’ between the particles’ input and output wavefunctions. Although the probability of finding a particle in a particular output path depends only on the amplitude of its wavefunction, the phase is important when determining the output wavefunction, and corresponding output probability, for two or more particles.
If two particles enter such a 50:50 beam-splitter, naively one would expect one of four possible outcomes: two in which the particles exit along a path together, and two in which they exit along different paths (Fig. 1b). In these cases, the single-particle output-wavefunction phases accumulate in an overall output phase. The HOM result is a consequence of the particles’ indistinguishability, which means that there is no measurable difference between the two outcomes in which the particles exit along different paths. The overall output phases of these indistinguishable outcomes are opposite to each other, and when added together using quantum rules for bosons (particles with integer spin, a quantum property common to both photons and helium-4 atoms), these two possible outcomes interfere and cancel. The only outcomes remaining are those with two particles in a single output. As a result, simultaneous single-particle detections (‘coincidence counts’) at both outputs are forbidden.
Lopes et al. demonstrate two-particle quantum interference with helium-4 atoms. In their experiments, the atoms’ paths are related to their speeds, which are manipulated by selectively transferring momentum to and from light in absorption and emission processes(5, 6). First, the researchers prepared a ‘twin pair’ by removing from an atom reservoir indistinguishable atoms with different speeds. Second, they used light pulses to modify the atoms’ momenta and cause the pair to meet; the atom in the first path travels with velocity v1 and the atom in the second path with v2. A beam-splitting mechanism implemented reflection and transmission by changing the atoms’ speeds with 50% probability from v1 to v2 and vice versa.
The atoms continued to travel until they hit a time-resolved, multipixel atom-counting detector, at which an atom with v1 would arrive at a different time from one with v2. Lopes and colleagues prepared many twin pairs in a short interval and recorded the precise location and timing of the atoms’ arrivals at the detector: a coincident count would be the measurement at a particular location of a particle at time t1 followed by a measurement at t2. Although the researchers found that the arrivals from the many pairs were distributed in two time windows (corresponding to the two output paths), they found a striking lack of instances among these random outcomes when the time difference was exactly t2t1, indicating that the atoms from a twin pair must be exiting the beam-splitter with the same velocity. This ‘anticorrelation’ is the signature of a HOM experiment.
As in quantum-optics demonstrations of the HOM effect, the present result demonstrates that pairs of identical, ‘quantum-entangled’ particles have been produced. The unique capabilities of this apparatus, including the combination of condensed metastable helium-4 atoms and the atom-counting detector, offer a spatial and temporal resolution unavailable to others. Protocols for transmitting and processing quantum information, analogous to those used in optical systems, can now be implemented with new capabilities in atomic systems: atoms, unlike photons, may interact with one another, and because they have mass, their mechanical properties, such as momentum, can be varied and used as experimental parameters.
Furthermore, because atoms can also be fermions (particles with half-integer spin, such as electrons), they could exhibit a quantum-interference effect that is the fermionic equivalent of the HOM effect(4). Evidence for this mechanism has already been seen in electronic systems(7). The bosonic HOM effect demonstrated here, and its fermionic counterpart, may offer new possibilities for implementing quantum-information protocols and for exploring the foundations of quantum physics.


(1) Hong, C. K., Ou, Z. Y. & Mandel, L. Phys. Rev. Lett. 59, 2044–2046 (1987).
(2) Lopes, R. et al. Nature 520, 66–68 (2015).
(3) Ou, Z. Y. & Mandel, L. Am. J. Phys. 57, 66 (1989).
(4) Loudon, R. Phys. Rev. A 58, 4904–4909 (1998).
(5) Campbell, G. K. et al. Phys. Rev. Lett. 96, 020406 (2006).
(6) Bonneau, M. et al. Phys. Rev. A 87, 061603 (2013).
(7) Neder, I. et al. Nature 448, 333–337 (2007).

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