Phonon arithmetic in a trapped ion system

Abstract

Single-quantum level operations are important tools to manipulate a quantum state. Annihilation or creation of single particles translates a quantum state to another by adding or subtracting a particle, depending on how many are already in the given state. The operations are probabilistic and the success rate has yet been low in their experimental realization. Here we experimentally demonstrate (near) deterministic addition and subtraction of a bosonic particle, in particular a phonon of ionic motion in a harmonic potential. We realize the operations by coupling phonons to an auxiliary two-level system and applying transitionless adiabatic passage. We show handy repetition of the operations on various initial states and demonstrate by the reconstruction of the density matrices that the operations preserve coherences. We observe the transformation of a classical state to a highly non-classical one and a Gaussian state to a non-Gaussian one by applying a sequence of operations deterministically.

Observation of Hopping and Blockade of Bosons in a Trapped Ion Spin Chain

“…In future experiments, this can be resolved by rotating the two principle axes of transverse motion (X and Y) with respect to the Raman beams such that only one mode is excited. For multi-phonon hopping experiments, it is also necessary to implement fast measurement of phonon distributions (instead of single phonon occupancy) using cascaded sideband pulses, as has been implemented on single ions [25,26].…”

Cross-Kerr Nonlinearity for Phonon Counting

“…In optics such methods include homodyning [1], photon counting [2] and photon number resolving detection [3,4]. In a trapped-ion system the motion of ions is usually probed by coupling it to the ion's internal state via a motional sideband transition, which enables reconstruction of phonon number distribution [5][6][7][8][9] or measurement of the parity of the motional state [10]. However most of the methods to determine the motional state are destructive in nature and the state of the oscillator after measurement does not correspond to its outcome.An ideal projective measurement should leave the quantum system immediately after measurement in the state defined by the measurement outcome.…”

Experimental quantum simulation of fermion-antifermion scattering via boson exchange in a trapped ion

“…The “uniform red sideband” 46 – 48 is implemented as an adiabatic transition where the transfer speed between and is the same for all n = 1, 2, …. It is realized by adding a time-dependent amplitude A ( t ) = sin( πt / d ) and a time-dependent phase φ ( t ) = −1/ β sin( πt / d ) to the normal red-sideband operation, and some additional terms to compensate for the AC Stark shift.…”

“…To measure , however, we need a phonon projective measurement 46 – 48 . Instead of using fluorescence detection together with a post-selection scheme, which may introduce significant heating errors because of photon scattering, here we use an auxiliary state as a swap buffer.…”

“…For the average boson number measurement, we first use optical pumping to trace out electronic states 48 and then apply a blue sideband time sweep from t = 0 to t = 12 π blue 50 . We get the phonon number distribution by fitting the result signals through the maximum likelihood method with parameters of the Fock state populations 46 , 47 . The main uncertainty in the average phonon measurement comes from fitting and we include one standard deviation as an uncertainty throughout the manuscript.…”