Quantum States Of Motion Research Articles

On the feasibility of detecting quantum delocalization effects on relativistic time dilation in optical clocks

Abstract We derive the predicted time dilation of delocalized atomic clocks in an optical lattice setup in the presence of a gravitational field to leading order in quantum relativistic corrections. We investigate exotic quantum states of motion whose relativistic time dilation is outside of the realm of classical general relativity, finding a regime where 24 Mg optical lattice clocks currently in development would comfortably be able to detect the special-relativistic contribution to the quantum effect (if the technical challenge of generating the necessary states can be met and the expected accuracy of such clocks can be attained). We find that the gravitational contribution, on the other hand, is negligible in this setup. We provide a detailed experimental protocol and analyse the effects of noise on our predictions. We also show that the magnitude of our predicted quantum time dilation effect remains just out of detectable reach for the current generation of 87 Sr optical lattice clocks. Our calculations agree with the predicted time dilation of classical general relativity when restricting to Gaussian states.

Precise control and non-destructive readout of quantum states of ion motion

Precise control and non-destructive readout of quantum states of ion motion

Quantum squeezing in a nonlinear mechanical oscillator

Mechanical degrees of freedom are natural candidates for continuous-variable quantum information processing and bosonic quantum simulations. However, these applications require the engineering of squeezing and nonlinearities in the quantum regime. Here we demonstrate squeezing below the zero-point fluctuations of a gigahertz-frequency mechanical resonator coupled to a superconducting qubit. This is achieved by parametrically driving the qubit, which results in an effective two-phonon drive. In addition, we show that the resonator mode inherits a nonlinearity from the off-resonant coupling with the qubit, which can be tuned by controlling the detuning. We, thus, realize a mechanical squeezed Kerr oscillator, in which we demonstrate the preparation of non-Gaussian quantum states of motion with Wigner function negativities and high quantum Fisher information. This shows that our results can also have applications in quantum metrology and sensing.

Matter-wave interferometers with trapped strongly interacting Feshbach molecules

We implement two types of matter-wave interferometers using trapped Bose-condensed Feshbach molecules, from weak to strong interactions. In each case, we focus on investigating interaction effects and their implications for the performance. In the Ramsey-type interferometer where interference between the two motional quantum states in an optical lattice is observed, interparticle interactions are found to induce energy shifts in the states. Consequently, this results in a reduction of the interferometer frequency and introduces a phase shift during the lattice pulses used for state manipulation. Furthermore, nonuniformity leads to dephasing and collisional effects contribute to the degradation of contrast. In the Michelson-type interferometer, where matter waves are spatially split and recombined in a waveguide, interference is observed in the presence of significant interaction, however coherence degrades with increasing interaction strength. Notably, coherence is also observed in thermal clouds, indicating the white-light nature of the implemented Michelson-type interferometer. Published by the American Physical Society 2024

Harnessing nonlinear dynamics for quantum state synthesis of mechanical oscillators in tripartite optomechanics

Owing to their long lifetimes at cryogenic temperatures, mechanical oscillators have been recognized as an attractive resource for quantum information science and as a test bed to explore fundamental physics. Key to many of these applications is the ability to prepare, manipulate, and measure quantum states of mechanical motion. By capturing the exact nonlinear quantum dynamics, we show how tripartite optomechanical interactions, involving the mutual coupling between two distinct optical modes and an acoustic resonance, enable quantum states of mechanical oscillators to be synthesized and interrogated using classical state preparation.

Tuneable Gaussian entanglement in levitated nanoparticle arrays

Optically levitated nanoparticles emerged as an interesting platform for probing fundamental physics. Quantum control of their motion (including potential shaping) predisposes them for emulating various physical systems and studying quantum phenomena with massive objects. Extending these capabilities to quantum many-body systems requires feasible strategies to couple and entangle nanoparticles directly or via an optical bus. We propose a variable, deterministic scheme to generate Gaussian entanglement in the motional steady state of levitated nanoparticles using coherent scattering. Coupling multiple nanoparticles to a common cavity mode allows cooling of a collective Bogoliubov mode; cooling multiple Bogoliubov modes (by trapping each nanoparticle in multiple tweezers, each scattering into a separate cavity mode) removes most thermal noise, leading to strong entanglement. Numerical simulations for three nanoparticles show great tuneability of entanglement with realistic experimental parameters. Our proposal paves the way towards complex motional quantum states for advanced quantum sensing protocols and many-body quantum simulations.

The manipulation of ultracold atoms of high orbitals in optical lattices

Ultracold atoms in optical lattices are a powerful tool for quantum simulation, precise measurement, and quantum computation. A fundamental problem in applying this quantum system is how to manipulate the higher bands or orbitals in Bloch states effectively. Here we mainly review our methods for manipulating high orbital ultracold atoms in optical lattices with different configurations. Based on these methods, we construct the atom-orbital qubit under nonadiabatic holonomic quantum control and Ramsey interferometry with trapped motional quantum states. Then we review the observation of the novel quantum states and the study of the dynamical evolution of the high orbital atoms in optical lattices. The effective manipulation of the high orbitals provides strong support for applying ultracold atoms in the optical lattice in many fields.

Determination of Multimode Motional Quantum States in a Trapped Ion System.

Trapped atomic ions are a versatile platform for studying interactions between spins and bosons by coupling the internal states of the ions to their motion. Measurement of complex motional states with multiple modes is challenging, because all motional state populations can only be measured indirectly through the spin state of ions. Here we present a general method to determine the Fock state distributions and to reconstruct the density matrix of an arbitrary multimode motional state. We experimentally verify the method using different entangled states of multiple radial modes in a five-ion chain. This method can be extended to any system with Jaynes-Cummings-type interactions.

Quantum scattering as a work source

We consider a collision between a moving particle and a fixed system, each having internal degrees of freedom. We identify the regime where the motion of the particle acts as a work source for the joint internal system, leading to energy changes which preserve the entropy. This regime arises when the particle has high kinetic energy and its quantum state of motion is broad in momentum and narrow in space, whether pure or mixed. In this case, the scattering map ruling the dynamics of the internal degrees of freedom becomes unitary and equivalent to that of a time-dependent interaction between the internal degrees of freedom of the colliding systems. It follows that the kinetic energy lost by the particle during the autonomous quantum collision coincides with the work performed by the time-dependent interaction. Recently, collisions with particles were shown to act as heat sources under suitable conditions; here we show that they can also act as work sources. This opens interesting perspectives for quantum thermodynamics formulations within scattering theory.

Parity measurement in the strong dispersive regime of circuit quantum acoustodynamics

Mechanical resonators are emerging as an important new platform for quantum science and technologies. A large number of proposals for using them to store, process and transduce quantum information motivates the development of increasingly sophisticated techniques for controlling mechanical motion in the quantum regime. By interfacing mechanical resonators with superconducting circuits, circuit quantum acoustodynamics can make a variety of important tools available for manipulating and measuring motional quantum states. Here we demonstrate the direct measurements of phonon number distribution and parity of non-classical mechanical states. We do this by operating our system in the strong dispersive regime, where a superconducting qubit can be used to spectroscopically resolve the phonon Fock states. These measurements are some of the basic building blocks for constructing acoustic quantum memories and processors. Furthermore, our results open the door for performing even more complex quantum algorithms using mechanical systems, such as quantum error correction and multimode operations. Mechanical resonators combined with superconducting circuits are a promising platform for controlling non-classical mechanical states. Here this platform is used to directly measure the parity of a motional quantum state.

Materials challenges for trapped-ion quantum computers

Trapped-ion quantum information processors store information in atomic ions maintained in position in free space by electric fields. Quantum logic is enacted through manipulation of the ions’ internal and shared motional quantum states using optical and microwave signals. Although trapped ions show great promise for quantum-enhanced computation, sensing and communication, materials research is needed to design traps that allow for improved performance by means of integration of system components, including optics and electronics for ion-qubit control, while minimizing the near-ubiquitous electric-field noise produced by trap-electrode surfaces. In this Review, we consider the materials requirements for such integrated systems, with a focus on problems that hinder current progress towards practical quantum computation. We give suggestions for how materials scientists and trapped-ion technologists can work together to develop materials-based integration and noise-mitigation strategies to enable the next generation of trapped-ion quantum computers. Trapped-ion qubits have great potential for quantum computation, but materials improvements are needed. This Review surveys materials opportunities to improve the performance of trapped-ion qubits, from understanding the surface science that leads to electric-field noise to developing methods for building ion traps with integrated optics and electronics.

Gravitational Forces Between Nonclassical Mechanical Oscillators

Interfacing quantum mechanics and gravity is one of the great open questions in natural science. Micromechanical oscillators have been suggested as a plausible platform to carry out these experiments. We present an experimental design aiming at these goals, inspired by Schm\"ole et al., Class. Quantum Grav. 33, 125031 (2016). Gold spheres weighing on the order a milligram will be positioned on large silicon nitride membranes, which are spaced at submillimeter distances from each other. These mass-loaded membranes are mechanical oscillators that vibrate at $\sim 2$ kHz frequencies in a drum mode. They are operated and measured by coupling to microwave cavities. First, we show that it is possible to measure the gravitational force between the oscillators at deep cryogenic temperatures, where thermal mechanical noise is strongly suppressed. We investigate the measurement of gravity when the positions of the gravitating masses exhibit significant quantum fluctuations, including preparation of the massive oscillators in the ground state, or in a squeezed state. We also present a plausible scheme to realize an experiment where the two oscillators are prepared in a two-mode squeezed motional quantum state that exhibits nonlocal quantum correlations and gravity the same time. Although the gravity is classical, the experiment will pave the way for testing true quantum gravity in related experimental arrangements. In a proof-of-principle experiment, we operate a 1.7 mm diameter Si$_3$N$_4$ membrane loaded by a 1.3 mg gold sphere. At 10 mK temperature, we observe the drum mode with a quality factor above half a million at 1.7 kHz, showing strong promise for the experiments. Following implementation of vibration isolation, cryogenic positioning, and phase noise filtering, we foresee that realizing the experiments is in reach by combining known pieces of current technology.

Motional quantum states of surface electrons on liquid helium in a tilted magnetic field

The Jaynes-Cummings model (JCM), one of the paradigms of quantum electrodynamics, was introduced to describe interaction between light and a fictitious two-level atom. Recently it was suggested that the JCM Hamiltonian can be invoked to describe the motional states of electrons trapped on the surface of liquid helium and subjected to a constant uniform magnetic field tilted with respect to the surface [Yunusova et al. Phys. Rev. Lett. 122, 176802 (2019)]. In this case, the surface-bound (Rydberg) states of an electron are coupled to the electron cyclotron motion by the in-plane component of tilted field. Here we investigate, both theoretically and experimentally, the spectroscopic properties of surface electrons in a tilted magnetic field and demonstrate that such a system exhibits a variety of phenomena common to the light dressed states of atomic and molecular systems. This shows that electrons on helium realize a prototypical atomic system where interaction between components can be engineered and controlled by simple means and with high accuracy, and which therefore can be potentially used as a new flexible platform for quantum experiments. Our work introduces a pure condensed-matter system of electrons on helium into the context of atomic, molecular and optical physics.

Non-classical energy squeezing of a macroscopic mechanical oscillator

Optomechanics and electromechanics have made it possible to prepare macroscopic mechanical oscillators in their quantum ground states, in quadrature squeezed states, and in entangled states of motion. In addition to coaxing ever larger and more tangible objects into a regime of quantum behavior, this new capability has encouraged ideas of using mechanical oscillators in the processing and communication of quantum information and as precision force sensors operating beyond the standard quantum limit. But the effectively linear interaction between motion and light or electricity precludes access to the broader class of quantum states of motion, such as cat states or energy squeezed states. Indeed, early optomechanical proposals noted the possibility to escape this restriction by creating strong quadratic coupling of motion to light. Although there have been experimental demonstrations of quadratically coupled optomechanical systems, these have not yet accessed nonclassical states of motion. Here we create nonclassical states by quadratically coupling motion to the energy levels of a Cooper-pair box (CPB) qubit. By monitoring the qubit's transition frequency, we detect the oscillator's phonon distribution rather than its position. Through microwave frequency drives that change both the state of the oscillator and qubit, we then dissipatively stabilize the oscillator in a state with a large mean phonon number of 43 and sub-Poissonian number fluctuations of approximately 3. In this energy squeezed state we observe a striking feature of the quadratic coupling: the recoil of the mechanical oscillator caused by qubit transitions, closely analogous to the vibronic transitions in molecules.

Phonon counting thermometry of an ultracoherent membrane resonator near its motional ground state

The generation of non-Gaussian quantum states of macroscopic mechanical objects is key to a number of challenges in quantum information science, ranging from fundamental tests of decoherence to quantum communication and sensing. Heralded generation of single-phonon states of mechanical motion is an attractive way toward this goal, as it is, in principle, not limited by the object size. Here we demonstrate a technique that allows for generation and detection of a quantum state of motion by phonon counting measurements near the ground state of a 1.5 MHz micromechanical oscillator. We detect scattered photons from a membrane-in-the-middle optomechanical system using an ultra-narrowband optical filter, and perform Raman-ratio thermometry and second-order intensity interferometry near the motional ground state ( n ¯ = 0.23 ± 0.02 p h o n o n s ). With an effective mass in the nanogram range, our system lends itself for studies of long-lived non-Gaussian motional states with some of the heaviest objects to date.

Quantum motional state tomography with nonquadratic potentials and neural networks

We propose to use the complex quantum dynamics of a massive particle in a non-quadratic potential to reconstruct an initial unknown motional quantum state. We theoretically show that the reconstruction can be efficiently done by measuring the mean value and the variance of the position quantum operator at different instances of time in a quartic potential. We train a neural network to successfully solve this hard regression problem. We discuss the experimental feasibility of the method by analyzing the impact of decoherence and uncertainties in the potential.

Optomechanical state reconstruction and nonclassicality verification beyond the resolved-sideband regime

Quantum optomechanics uses optical means to generate and manipulate quantum states of motion of mechanical resonators. This provides an intriguing platform for the study of fundamental physics and the development of novel quantum devices. Yet, the challenge of reconstructing and verifying the quantum state of mechanical systems has remained a major roadblock in the field. Here, we present a novel approach that allows for tomographic reconstruction of the quantum state of a mechanical system without the need for extremely high quality optical cavities. We show that, without relying on the usual state transfer presumption between light an mechanics, the full optomechanical Hamiltonian can be exploited to imprint mechanical tomograms on a strong optical coherent pulse, which can then be read out using well-established techniques. Furthermore, with only a small number of measurements, our method can be used to witness nonclassical features of mechanical systems without requiring full tomography. By relaxing the experimental requirements, our technique thus opens a feasible route towards verifying the quantum state of mechanical resonators and their nonclassical behaviour in a wide range of optomechanical systems.

Classical and quantum dynamics of a trapped ion coupled to a charged nanowire

We study theoretically the mechanical drive of a trapped ultracold ion by a charged nanowire through their mutual Coulomb interaction. We characterize the perturbation of the trapping potential for the ion by the nanowire and discuss the parameters determining the dynamics of the ion under the action of the nanooscillator. We explore the classical dynamics as well as motional quantum states of the ion which can be generated and manipulated with the resonant drive of the nanowire and the effects of anharmonicities of the ion-trap potential on the system. Our modelling indicates that unusual quantum states of the ion motion can be generated with this approach and that sympathetic cooling and quantum entanglement can be realised when both subsystems operate in the quantum regime. The present ion-mechanical hybrid system might prove interesting as a new quantum device, for quantum sensing experiments, for spectroscopy and for mass spectrometry.

Creation and control of multi-phonon Fock states in a bulk acoustic-wave resonator.

Quantum states of mechanical motion can be important resources for quantum information, metrology and studies of fundamental physics. Recent demonstrations of superconducting qubits coupled to acoustic resonators have opened up the possibility of performing quantum operations on macroscale motional modes1-3, which can act as long-lived quantum memories or transducers. In addition, they can potentially be used to test decoherence mechanisms in macroscale objects and other modifications to standard quantum theory4,5. Many of these applications call for the ability to create and characterize complex quantum states, such as states with a well defined phonon number, also known as phonon Fock states. Such capabilities require fast quantum operations and long coherence times of the mechanical mode. Here we demonstrate the controlled generation of multi-phonon Fock states in a macroscale bulk acoustic-wave resonator. We also perform Wigner tomography and state reconstruction to highlight the quantum nature of the prepared states6. These demonstrations are made possible by the long coherence times of our acoustic resonator and our ability to selectively couple a superconducting qubit to individual phonon modes. Our work shows that circuit quantum acoustodynamics7 enables sophisticated quantum control of macroscale mechanical objects and opens up the possibility of using acoustic modes as quantum resources.

Ramsey interferometry with trapped motional quantum states

Ramsey interferometers using internal electronic or nuclear states find wide applications in science and engineering. We develop a matter wave Ramsey interferometer for trapped motional quantum states exploiting the s- and d-bands of an optical lattice and study it both experimentally and theoretically, identifying the different de-phasing and de-coherence mechanisms. Implementing a band echo technique, employing repeated π-pulses we suppress the de-phasing evolution and significantly increase the coherence time of the trapped state interferometer by one order of magnitude. Thermal fluctuations are the main mechanism for the remaining decay of the contrast. Our demonstration of an echo-Ramsey interferometer with trapped quantum states in an optical lattice has potential application in the study of quantum many-body lattice dynamics, and motional qubits manipulation.