Hong–Ou–Mandel interference of two phonons in trapped ions

Abstract

The quantum statistics of bosons and fermions manifest themselves in the manner in which two indistinguishable particles interfere quantum mechanically. When two photons, which are bosonic particles, enter a beam-splitter with one photon in each input port, they bunch together at either of the two output ports. The corresponding disappearance of the coincidence count is the Hong-Ou-Mandel effect. Here we show the phonon counterpart of this effect in a system of trapped-ion phonons, which are collective excitations derived by quantizing vibrational motions that obey Bose-Einstein statistics. We realize a beam-splitter transformation of the phonons by employing the mutual Coulomb repulsion between ions, and perform a two-phonon quantum interference experiment using that transformation. We observe an almost perfect disappearance of the phonon coincidence between two ion sites, confirming that phonons can be considered indistinguishable bosonic particles. The two-particle interference demonstrated here is purely a quantum effect, without a classical counterpart, hence it should be possible to demonstrate the existence of entanglement on this basis. We attempt to generate an entangled state of phonons at the centre of the Hong-Ou-Mandel dip in the coincidence temporal profile, under the assumption that the entangled phonon state is successfully generated if the fidelity of the analysis pulses is taken into account adequately. Two-phonon interference, as demonstrated here, proves the bosonic nature of phonons in a trapped-ion system. It opens the way to establishing phonon modes as carriers of quantum information in their own right, and could have implications for the quantum simulation of bosonic particles and analogue quantum computation via boson sampling.

Quantum Optics of Spin Waves through ac Stark Modulation

“…The Hong-Ou-Mandel (HOM) interference [1] is an inherently quantum two-particle effect serving as an important test of both nonclassicality of the input state as well as proper operation of the beamsplitter. While nowadays it is easily achievable with photons, recent experiments demonstrated similar quantum-interferometric properties of atoms [2][3][4], phonons [5,6], plasmons [7,8] and photons but in elaborate hybrid systems [6,[9][10][11][12][13][14]. This progress illuminates the perspective to combine linear operations, that have always been simple for photons, and nonlinear operations, that can be engineered in material systems.…”

Modeling the atomtronic analog of an optical polarizing beam splitter, a half-wave plate, and a quarter-wave plate for phonons of the motional state of two trapped atoms

“…Moreover, mechanical damping is of the order of several seconds, but we have estimated the duration of our scheme to be of the order of microseconds, so the mechanical damping can be neglected, too. On the other hand, long-range dipole-dipole interaction between the two Rydberg atoms can also be neglected, because it is proportional to (1/r) 6 and P 4 , where r and P are the distance between the atoms and dipole moment of the atoms, respectively. The dipole moment of the Rydberg atoms is proportional to a 0 n 2 , in which a 0 is the Bohr radius and n is the principal quantum number.…”

“…They can be used to encode information as qubits because of their appealing properties such as low-propagation speed, which provides us with new schemes for processing quantum information, and their short wavelength, which allows us to access regimes of atomic physics that cannot be reached in photonic systems [1]. Numerous researchers are trying to find ways of using phonons for quantum information and computation and, more importantly, finding ways for manipulating the quantum information that is carried by these phonons [2,3,4,5,6,7].…”

Protocol for Implementing Quantum Nonparametric Learning with Trapped Ions

“…As for two ions, besides the standard controlled-NOT gate [38], a beam-splitter defined as B(θ) = e iθ(a † jα aj+1α+a † j+1α ajα) is needed, and it was theoretically proposed [37] and then experimentally achieved recently [48]. These two operators thus couple qubit states or qumodes from different ions.…”