Revealing Quantum Statistics with a Pair of Distant Atoms

Abstract

Quantum statistics have a profound impact on the properties of systems composed of identical particles. At the most elementary level, Bose and Fermi quantum statistics differ in the exchange phase, either 0 or π, which the wavefunction acquires when two identical particles are exchanged. In this Letter, we demonstrate that the exchange phase can be directly probed with a pair of massive particles by physically exchanging their positions. We present two protocols where the particles always remain spatially well separated, thus ensuring that the exchange contribution to their interaction energy is negligible and that the detected signal can only be attributed to the exchange symmetry of the wavefunction. We discuss possible implementations with a pair of trapped atoms or ions.The symmetrization postulate of quantum mechanics asserts that the wavefunction of a system of identical particles is either completely symmetric or antisymmetric under particle exchange [1]. A plethora of physical phenomena observed in experiments investigating atoms, molecules and solids, as well as the statistical properties of light supports the (anti)symmetrization requirement. While more general quantum statistics [2] are in principle conceivable, they seem not to be realized by elementary particles in nature [3].The influence of the wavefunction symmetry has been spectacularly demonstrated in few-particle systems with Hong-Ou-Mandel-like interference experiments [4][5][6][7][8], and in many-body systems with ultracold quantum gases [9]. Spectroscopic experiments have also tested the symmetrization postulate for massive particles [10][11][12][13][14] and for photons [15,16] with high precision. Recently, exchange interactions have been applied in engineered quantum systems for entangling pairs of atoms or electrons [17][18][19][20].At the most elementary level, the wavefunction symmetry manifests itself when two identical particles are exchanged in position [ Fig. 1(a)]: Their state acquires an exchange phase ϕ ex , which is 0 for bosons but π for fermions. Exchange of identical particles can naturally occur in molecules where identical, distant nuclei may be interchanged as a result of a rotation [21]. Prior experiments [10][11][12][13][14] have exploited this naturally occurring exchange of identical particles to show that only certain rotational states are permitted by the symmetrization postulate. However, a direct interferometric measurement of the exchange phase ϕ ex has never been attempted. In this Letter, we propose to use the high controllability of trapped atoms or ions for a direct measurement of this * christian.roos@uibk.ac.at † alberti@iap.uni-bonn.de phase. To this end, we devise experiments where the twoparticle wavefunction is superposed with the wavefunction of the same particles having swapped positions. We further request that, if the interferometric sequence is interrupted at any time, the two particles are always found at distant positions. This condition of vanishing overlap between the two particles ensures that...

Endurance of quantum coherence due to particle indistinguishability in noisy quantum networks

“…Formally, such coherences do not represent manipulable superpositions, but their presence in the steady state implies that the particles retain their capability to interfere (indistinguishability) in experiments of the Hong-Ou-Mandel type [48,49,52,53]. Indeed, it has been shown that superpositions originated from the exchange symmetry can become accessible and exploitable [48,[54][55][56][57].…”

Signatures of Indistinguishability in Bosonic Many-Body Dynamics

“…This fundamental question is, however, key to a variety of complex quantum phenomena, such as dynamical equilibration after a quench [34][35][36], correlation formation [37,38], or transport in interacting many-body systems [39,40]. Furthermore, certification of the bosonic, fermionic, as well as (in)distinguishable character of particles [12,14,[41][42][43][44] could also be achieved by identifying the corresponding interference fingerprints in the (interacting) dynamics.Hence, it is the purpose of this work to systematically explore the impact of particles' indistinguishability on the time evolution of interacting many-body systems. We consider bosons which occupy a discrete set of coupled modes and whose mutual (in)distinguishability is controlled by an additional internal degree of freedom.…”

Coherent Control of the Rotational Degree of Freedom of a Two-Ion Coulomb Crystal

“…The energy spectrum of the angular momentum eigenstates is quadratic in quantum number, increasing the complexity possible in Hamiltonian engineering and enabling the simulation of rotational dynamics of diatomic molecules [4][5][6]. Moreover, the periodic boundary conditions of angular momentum states enable fundamentally new operations such as the deterministic coherent exchange of the ions' wave functions [7] and the ability to create interferometry geometries new to ions [8,9]. Rotational states also have fundamental physics applications in Aharanov-Bohm style experiments because of their enclosed area [10,11] and in observing Hawking radiation in acoustic analogs of black holes [12,13].…”

“…For example, at a Ramsey time t revival = π ωr∆ , the phase of each superposition becomes an integer multiple of 2π, manifesting as a revival in the contrast of the excitation. Taking advantage of the symmetrization requirement to create a fully odd or even rotational mode occupation under particle exchange would induce an additional revival at t revival /2, which would demonstrate the indistiguishability of the two 40 Ca + ions even as they are separated by 6.27 µm at all times [7,26].…”