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arXiv:1911.05810 · Physical Review A

State-dependent motional squeezing of a trapped ion: Proposed method and applications

Martín Drechsler, M. Belén Farías, Nahuel Freitas, Christian Tomás Schmiegelow, Juan Pablo Paz

Published May 18, 2020• 23 citations
arXivHTMLPDF

Abstract

We show that the motion of a cold trapped ion can be squeezed by modulating the intensity of a phase-stable optical lattice placed inside the trap. The method we propose is reversible (unitary) and state selective: it effectively implements a controlled-squeeze gate. This resource could be useful for quantum information processing with continuous variables. We show that the controlled-squeeze gate can prepare coherent superpositions of states which are squeezed along complementary quadratures. Furthermore, we show that these states, which we denote ``$\mathcal{X}$ states,'' exhibit a high sensitivity to small displacements along two complementary quadratures, which makes them useful for quantum metrology.

DOI
10.1103/physreva.101.052331

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We show that the motion of a cold trapped ion can be squeezed by modulating the intensity of a phase-stable optical lattice placed inside the trap. The method we propose is reversible (unitary) and state selective: it effectively implements a controlled-squeeze gate. This resource could be useful for quantum information processing with continuous variables. We show that the controlled-squeeze gate can prepare coherent superpositions of states which are squeezed along complementary quadratures. Furthermore, we show that these states, which we denote ``X\mathcal{X}X states,'' exhibit a high sensitivity to small displacements along two complementary quadratures, which makes them useful for quantum metrology.
We demonstrate a state-dependent Gaussian gate set on the motional modes of trapped 40^{40}40Ca+^++ ions, realized with an optical tweezer. Dynamic control of the tweezer intensity and position enables local displacement, squeezing, phase-space rotation, and beamsplitter operations, constituting a complete gate set. By varying the tweezer position relative to the ion, we show how the strength of each operation is set by the corresponding spatial derivative of the local optical potential. We further demonstrate the inherent dependence of each operation on the ion's internal state and use coherent spin-motion coupling provided by the tweezer to create a motional cat state. Our work establishes optical tweezers as a unified and local resource for continuous-variable quantum control in trapped ion systems.
Entangling gates are an essential component of quantum computers. However, generating high-fidelity gates, in a scalable manner, remains a major challenge in all quantum information processing platforms. Accordingly, improving the fidelity and robustness of these gates has been a research focus in recent years. In trapped ions quantum computers, entangling gates are performed by driving the normal modes of motion of the ion chain, generating a spin-dependent force. Even though there has been significant progress in increasing the robustness and modularity of these gates, they are still sensitive to noise in the intensity of the driving field. Here we supplement the conventional spin-dependent displacement with spin-dependent squeezing, which creates a new interaction, that enables a gate that is robust to deviations in the amplitude of the driving field. We solve the general Hamiltonian and engineer its spectrum analytically. We also endow our gate with other, more conventional, robustness properties, making it resilient to many practical sources of noise and inaccuracies.
Trapped ions offer a pristine platform for quantum computation and simulation, but improving their coherence remains a crucial challenge. Here, we propose and analyze a new strategy to enhance the coherent interactions in trapped ion systems via parametric amplification of the ions' motion-by squeezing the collective motional modes (phonons), the spin-spin interactions they mediate can be significantly enhanced. We illustrate the power of this approach by showing how it can enhance collective spin states useful for quantum metrology, and how it can improve the speed and fidelity of two-qubit gates in multi-ion systems, important ingredients for scalable trapped ion quantum computation. Our results are also directly relevant to numerous other physical platforms in which spin interactions are mediated by bosons.
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.
In quantum optics, squeezing corresponds to the process in which fluctuations of a quadrature operator are reduced below the shot noise limit. In turn, nonlinear squeezing can be defined as reduction of fluctuations related to nonlinear combination of quadrature operators. Quantum states with nonlinear squeezing are a necessary resource for deterministic implementation of high-order quadrature phase gates that are, in turn, sufficient for advanced quantum information processing. We demonstrate that this class of states can be deterministically prepared by employing a single self-Kerr gate accompanied by suitable Gaussian processing. The required Kerr coupling depends on the energy of the initial system and can be made arbitrarily small. We also employ numerical simulations to analyze the effects of imperfections and to show to which extent can they be neglected.
We present a theoretical model for realizing squeezed lasing in a trapped-ion system without relying on engineered baths or tailored dissipative reservoirs. Our approach leverages the intrinsic ion-phonon interactions, where two trapped ions, each interacting with a shared vibrational mode, are driven on both red- and blue-sideband transitions. This enables the creation of a squeezed state of motion through the dynamic coupling between the ions' internal states and the phonon mode. Unlike traditional methods that require bath engineering, our model demonstrates that squeezed lasing can be achieved through a direct manipulation of ion-phonon interactions, with no external reservoirs required. We explore the steady-state behavior of the system, analyzing the onset of lasing, gain-loss balance, and the role of the squeezing parameter in shaping the phonon field's statistical properties. Furthermore, we show how external coherent drives can stabilize phase coherence and achieve controlled quadrature squeezing, offering a simple yet effective method for achieving squeezed lasing in quantum mechanical systems. Our findings provide new insights into the realization of squeezed states in phonon-based systems, with potential applications in quantum metrology and information processing.