Motional Fock states for quantum-enhanced amplitude and phase measurements with trapped ions

Abstract

The quantum noise of the vacuum limits the achievable sensitivity of quantum sensors. In non-classical measurement schemes the noise can be reduced to overcome this limitation. However, schemes based on squeezed or Schrödinger cat states require alignment of the relative phase between the measured interaction and the non-classical quantum state. Here we present two measurement schemes on a trapped ion prepared in a motional Fock state for displacement and frequency metrology that are insensitive to this phase. The achieved statistical uncertainty is below the standard quantum limit set by quantum vacuum fluctuations, enabling applications in spectroscopy and mass measurements.

Detection of the 5p – 4f orbital crossing and its optical clock transition in Pr9+

“…If the HCI is in the target state, the ODF exerts an oscillating force onto the HCI. This displaces its motional state, which can be detected efficiently on the co-trapped Be ion 23,33 , further enhanced by employing non-classical states of motion 34 . We estimate an achievable displacement rate of tens of kHz exciting coherent states of motion for realistic parameters of laser radiation at 408 nm detuned by 1 MHz from the P – F transition.…”

Metrological Nonlinear Squeezing Parameter

“…Spin squeezing is also a witness of metrologicallyuseful multiparticle-entanglement [23][24][25][26] and Bell correlations [27][28][29]. Squeezing of linear observables of discrete [23][24][25][26][30][31][32][33][34][35][36][37] or continuous variables [38][39][40][41][42], e.g., collective spins or quadratures, has proven to be a successful concept to characterize the class of Gaussian quantum states with phase-estimation sensitivities beyond the classical limit [3], and is hereinafter indicated as metrological linear squeezing.Yet, some highly sensitive continuous-variable states are non-Gaussian [43][44][45][46] and Gaussian spin states form a small and non-optimal class of useful states for quantum metrology [47][48][49]. Non-Gaussian states further hold the promise of opening up classically intractable pathways for quantum information processing [50][51][52].…”

“…Yet, some highly sensitive continuous-variable states are non-Gaussian [43][44][45][46] and Gaussian spin states form a small and non-optimal class of useful states for quantum metrology [47][48][49]. Non-Gaussian states further hold the promise of opening up classically intractable pathways for quantum information processing [50][51][52].…”

“…Nonlinear continuos-variable squeezing parameters and Fock-state sensing.-In the continuous variable case, the nonlinear squeezing coefficient is defined from higher-order combinations ofx = (â +â † )/ √ 2 andp = i(â † −â)/ √ 2, i.e., phase space quadrature operators for a bosonic single-mode field with annihilation operatorâ [82]. A particularly important application is the sensing of displacement amplitudes, which can be used to estimate small forces and fields [46]. Displacements are generated by linear combinations ofx and p, i.e.,D(α) = exp(αâ † − α * â ) = exp (iq n θ).…”

Coherently displaced oscillator quantum states of a single trapped atom

“…We anticipate that the basic concepts exhibited in this work can be transferred to many other HO systems and foresee various extensions and refinements of the current work. For example, it should be possible to find interesting modifications of the coherent displacement sequences by utilizing different displacement patterns in phase space or by displacing non-classical quantum states [33,34].…”