We demonstrate control of a trapped-ion quantum harmonic oscillator in a squeezed Fock state basis, using engineered Hamiltonians analogous to the Jaynes-Cummings and anti-Jaynes-Cummings forms. We demonstrate that for squeezed Fock states with low n the engineered Hamiltonians reproduce the sqrt[n] scaling of the matrix elements which is typical of Jaynes-Cummings physics, and also examine deviations due to the finite wavelength of our control fields. Starting from a squeezed vacuum state, we apply sequences of alternating transfer pulses which allow us to climb the squeezed Fock state ladder, creating states up to excitations of n=6 with up to 8.7 dB of squeezing, as well as demonstrating superpositions of these states. These techniques offer access to new sets of states of the harmonic oscillator which may be applicable for precision metrology or quantum information science.
We demonstrate control of a trapped-ion quantum harmonic oscillator in a squeezed Fock state basis, using engineered Hamiltonians analogous to the Jaynes-Cummings and anti-Jaynes-Cummings forms. We demonstrate that for squeezed Fock states with low n the engineered Hamiltonians reproduce the sqrt[n] scaling of the matrix elements which is typical of Jaynes-Cummings physics, and also examine deviations due to the finite wavelength of our control fields. Starting from a squeezed vacuum state, we apply sequences of alternating transfer pulses which allow us to climb the squeezed Fock state ladder, creating states up to excitations of n=6 with up to 8.7 dB of squeezing, as well as demonstrating superpositions of these states. These techniques offer access to new sets of states of the harmonic oscillator which may be applicable for precision metrology or quantum information science.
Summary form only given, as follows. The ability to create and completely characterize a variety of fundamental quantum states has long been sought after in the laboratory since it brings to the forefront issues involving the relationship between quantum and classical physics. The interaction of a trapped atom with classical laser light constitutes a simple and well-isolated quantum system that makes experiments along these lines possible. The motion of an ion trapped in a rf-trap can be described as a quantum harmonic oscillator. If the ion is driven by a classical light field, several interactions similar to and beyond the simple Jaynes-Cummings coupling can be realized. These couplings allow for precisely controlled engineering and measurement of quantum states. We create states having both classical and nonclassical character including thermal, number, coherent, squeezed, and Schrodinger cat states. The motional quantum state is fully reconstructed with use of two novel schemes that determine the density matrix in the number state basis and the Wigner function. Our techniques allow well-controlled experiments on decoherence and related phenomena on the quantum-classical borderline.
We demonstrate an optimal quantum control strategy for the deterministic preparation of entangled harmonic oscillator states in trapped ions. The protocol employs dynamical phase modulation of laser-driven Jaynes-Cummings and anti-Jaynes-Cummings interactions. We prepare two-mode squeezed vacuum states in the motions of a trapped ion and characterize the states with phase-space tomography. We verify continuous-variable entanglement by measuring an Einstein-Podolsky-Rosen entanglement parameter of 0.0132(7), which surpasses the threshold of 0.25 for Reid's Einstein-Podolsky-Rosen criterion. We also perform a continuous-variable Bell test and find a violation of the Clauser-Horne-Shimony-Holt inequality, measuring 2.26(3), exceeding the entanglement threshold of 2. We also demonstrate the flexibility of our method by preparing a non-Gaussian entangled oscillator state-a superposition of two-mode squeezed vacuum states.
Quantum harmonic oscillators are a central resource in quantum technologies. Coupling this resource to a two-level system gives rise to spin-oscillator dynamics that can be used for system calibrations, enhanced sensitivity to signals, and the preparation of oscillator entangled states. Chapter 4 introduces a motional-frequency calibration protocol based on a time-reversal, state-dependent force sequence that maps the effects of motional-frequency miscalibration onto a narrow spin-response feature. The chapter also discusses how thermally occupied motional states enhance sensitivity to particular Hamiltonian terms, making them effective probe states. A two-point feedback servo with processing performed on a field-programmable gate array, or FPGA, is used to track the interaction resonance in real time, enabling sub-second updates and continuous correction of frequency drift during data acquisition. Chapter 5 realizes phase-insensitive displacement sensing by embedding spin-dependent squeezing in a time-reversal interferometry sequence. The method prepares a spin-correlated superposition of orthogonally squeezed motional states, yielding a spin-observable response used to estimate displacement amplitudes while remaining agnostic to the signal phase. Experiments with vacuum and number-state probes demonstrate enhanced sensitivity with increasing motional energy. Chapter 6 extends the spin-oscillator toolkit to multi-oscillator control. Optimized phase modulations applied to Jaynes-Cummings and anti-Jaynes-Cummings couplings between a single spin and two motional modes synthesize an effective two-mode squeezing interaction, enabling preparation of two-mode squeezed vacuum states and a non-Gaussian superposition of those states. Joint phase-space tomography reveals multi-mode correlations, and continuous-variable entanglement is certified by the Einstein-Podolsky-Rosen criterion and a Clauser-Horne-Shimony-Holt-type continuous-variable Bell test.
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.
The robust generation of quantum states in the presence of decoherence is a primary challenge for explorations of quantum mechanics at larger scales. Using the mechanical motion of a single trapped ion, we utilize reservoir engineering to generate squeezed, coherent, and displaced-squeezed states as steady states in the presence of noise. We verify the created state by generating two-state correlated spin-motion Rabi oscillations, resulting in high-contrast measurements. For both cooling and measurement, we use spin-oscillator couplings that provide transitions between oscillator states in an engineered Fock state basis. Our approach should facilitate studies of entanglement, quantum computation, and open-system quantum simulations in a wide range of physical systems.
A single ion trapped in a harmonic potential and laser cooled at the node of a standing wave can be described in terms of the Jaynes-Cummings Hamiltonian known in quantum optics. Similar to nonclassical states of light we propose to prepare nonclassical states of the ion motion in a harmonic trap. In particular, several schemes for the preparation of Fock states are presented, and techniques for the preparation of squeezed states and coherent states of the ion motion are indicated. For an observation of these nonclassical states we propose to measure quantum collapse and revival in the population inversion of a single trapped ion.