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.
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.
Quantum noise is a fundamental limitation for quantum sensors and results in the so-called shot-noise limit. Nowadays, several systems such as optical clocks or gravitational wave detectors approach measurement sensitivities where this limitation poses a major contribution to the total statistical uncertainty. It is known that this limit can be overcome by preparing the probe in a non-classical state. We will give an overview over the different non-classical states that have been implemented in the motion of single trapped ions and discuss their individual advantages and limitations in metrology. Possible applications for the presented experiments are the measurement of small oscillating electric fields and trapping frequencies. The Focus will be on our experimental work on Fock states, where quantum-enhanced sensing in both scenarios is possible with the same quantum state.
A trapped-ion harmonic oscillator represents a rich and well-controlled platform for tests of quantum physics, with applications to quantum simulations, quantum sensing, and quantum information processing. Owing to its net charge, the ion's motion is affected by changes in the electric potential. Consequently, electric field and potential curvature noise will limit the coherence of the ion's harmonic oscillation. While in some respects, this serves as a limitation in the performance of the trapped ion system (for example, in the fidelity of two-qubit gates or quantum simulations with motional quanta), it also opens an opportunity to use the ion as a precise field sensor and to use engineered quantum states of motion to enhance the sensitivity to these fields beyond the standard quantum limit (SQL). This thesis describes the implementation of such applications on a single beryllium ion confined in a Paul trap. In the thesis, I present the theory of an ideal harmonic oscillator and the implementation of this system using the motion of a single trapped ion, including producing special quantum states of motion; these states include the energy eigenstates of the harmonic oscillator, called number states, up to n=100, superpositions of number states of the form (1/√2)(|0> + |n>), with n up to 18, and coherently displaced number states with an average occupation up to approximately 300. I describe how we use these quantum states of motion for precise sensing of fluctuations of the harmonic oscillator frequency. The sensitivity of the (1/√2)(|0> + |n>) state ideally follows the 1/n Heisenberg scaling for frequency sensitivity. Additionally, I describe investigations of the spectrum of motional frequency noise using a series of coherent displacements of the motion of the ion, with features similar to Ramsey and dynamical decoupling sequences for two-level systems. While these displaced states don't improve sensitivity over the SQL, they can be simply and rapidly implemented with trapped ions. I discuss extensions to all of these experiments, including to multiple ions in a new trap designed to confine 3 or 4 ions in individually tunable potential wells.
Abstract We present a protocol to produce a class of non-thermal Fock state mixtures in trapped ions. This class of states features a clear metrological advantage with respect to the ground state, thus overcoming the standard quantum limit without the need for full sideband cooling and Fock-state preparation on a narrow electronic transition. The protocol consists in the cyclic repetition of red-sideband (RSB), measurement and preparation laser pulses. By means of the Kraus map representation of the protocol, it is possible to relate the length of the RSB pulses to the specific class of states that can be generated. With the help of numerical simulations, we analyse the parametric regime where these states can be reliably reproduced.
We discuss a simple implementation of a quantum nondemolition measurement of the vibronic state of a trapped ion. This scheme allows the production of Fock states associated to the center-of-mass motion and the determination of the population distribution of the trap levels, and is based on the vibronic level dependence of the frequency of Rabi oscillations between two internal states of the ion, induced by a resonant carrier field. The same scheme can be used to produce a Schr\"odinger-cat-like state after a single interaction between the trapped ion and the carrier pulse, followed by the detection of the ionic internal state. \textcopyright{} 1996 The American Physical Society.
The purpose of this work is to investigate methods by which the quantum states of trapped ions may be better controlled and measured for the applications of quantum computing, quantum simulation, and the generation of atomic frequency standards. We report on two primary projects: first, we control the relative coupling strengths of carrier and first-order motional sideband interactions of a trapped ion by placing it in a resonant optical standing wave. Our configuration uses the surface of a microfabricated chip trap as a mirror, avoiding the technical challenges of in-vacuum optical cavities. Displacing the ion along the standing wave, we show a periodic suppression of the carrier and sideband transitions, with the cycles for the two cases 180◦ out of phase with each other. This technique allows for the suppression of off-resonant carrier excitations when addressing the motional sidebands, and has applications in quantum computation and quantum simulation. Second, we investigate methods proposed in Ref. [36] which may improve the performance of trapped ion (or atom) frequency standards when the interrogating local oscillator is of limited quality. These methods could be applied to future generations of small-scale frequency standards, which are in demand for applications such as local GPS networks and distributed sensors. We propose a scheme for implementing these methods in a 40Ca+ based frequency standard, and outline the technical requirements for doing so. Finally, we present preliminary results characterizing single-ion coherence times and ion “state destruction” events in our system, and discuss how they will affect the realization of the proposed scheme.
We report the creation and full determination of several quantum states of motion of a 9Be+ ion bound in a RF (Paul) trap. The states are coherently prepared from an ion which has been initially laser cooled to the zero-point of motion. We create states having both classical and non-classical character including thermal, number, coherent, squeezed, and ‚Schrödinger cat‘ states. The motional quantum state is fully reconstructed using two novel schemes that determine the density matrix in the number state basis or the Wigner function. Our techniques allow well controlled experiments decoherence and related phenomena on the quantum-classical borderline.