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Simulating 2d Spin Lattices with Ion Crystals

Periodic Reporting for period 4 - SPICY (Simulating 2d Spin Lattices with Ion Crystals)

Reporting period: 2022-03-01 to 2023-11-30

At the level of the individual constituents of matter, the behavior of our world is governed by quantum mechanics. The field of quantum-many body physics investigates systems of particles that interact with each other according to the laws of quantum physics. Examples for such systems are magnetic particles interacting with each other in a solid or electrons interacting with each other in an atom or molecule. Though the basic equations describing the interactions between the constituents are simple, they can be extremely challenging to analyze and impossible to simulate numerically for systems that only contain a few tens of particles.
Quantum simulation – the approach to use a well-controlled experimental quantum many-particle system to get insights into the physics of a model Hamiltonian of interest – promises to elucidate problems which are too hard to solve for classical computers. In a quantum simulator, information is encoded in a collection of quantum systems (qubits) and processed by a series of quantum operations coupling the qubits. This scheme requires an interacting quantum many-body system with near-perfect control over the interaction between its individual constituents.
The experimental investigation of quantum many-body systems is being studied for at least two reasons: on the one hand, simple interactions between identical quantum particles can give rise to a bewildering complexity of emergent physical phenomena, which are theoretically hard to understand or to predict. On the other hand, the processing of information based on the laws of quantum physics has led to a new model of computation whose computational power is superior to the classical one. Important optimization problems, which might arise in an industrial context, can be mapped to the dynamics of many-particle problems in this way.
Within this project, we develop trapped-ion based quantum simulations to larger numbers of particles by constructing an experimental apparatus capable of manipulating two-dimensional ion crystals containing 50-100 particles with quantum control over each individual ion. The approach pursued is to encode quantum information in the electronic states of an ensemble of trapped and laser-cooled ions, to process the information by means of laser pulses that couple the quantum state of the ions to each other, and to read out the information by fluorescence measurements. This approach necessitates the development of a new ion trap apparatus and of novel technique for manipulating the ions. The new device is used for carrying out quantum simulations by investigating non-equilibrium quantum dynamics of the trapped ions in a regime that is inaccessible to exact numerical simulations.
Conclusions: The performed work has shown that radiofrequency traps constitute an excellent tool for creating 2d-ion crystals in the quantum domain despite the ions experiencing strong driven motion. Planar crystals with over 100 ions could be reliably trapped without undergoing frequent changes of the lattice geometry; all transverse motional modes of the crystals can be laser-cooled close to their ground state. The project demonstrated the engineering of effective spin-spin interactions between the ions in crystals with more than 100 ions for the study of quantum non-equilibrium dynamics in a regime, where exact numerical simulations of the quantum dynamics are expected to fail. The generation of entanglement in crystals with up to 100 ions could be demonstrated by realization of spin-squeezed quantum states created by finite-range interactions of XY type
We designed the centerpiece of the new setup, a novel monolithic 3D linear Paul trap (Fig. 1), and had it fabricated using subtractive 3d printing and subsequent metallization for defining the trap electrodes. The trap geometry was designed to (1) provide good optical access to the ions, (2) feature low distortions of the trapping potential by terms that might couple energy into the ion motion, (3) enable efficient laser cooling, and (4) orient the electric field lines in a way that minimizes the influence of driven ion motion on quantum operations.
For housing the trap, we developed and built a new compact vacuum chamber (Fig. 2a) with excellent optical access and ultra-high vacuum. All laser sources for manipulating the ions were integrated into optical setups (Fig.2b) for addressing the ions by laser pulses. For coherent excitation, the laser pulse properties are controlled by a novel versatile radiofrequency source integrated into the experiment control program.
In an existing apparatus, random measurements were used to measure purities and entanglement properties of crystals with up to 20 ions (Science 364, 260 (2019)), demonstrating a cross-platform verification protocol (PRL 124, 010504 (2020)) and measuring quantum information scrambling (PRL 124, 240505 (2020)). Secondly, we demonstrated variational simulation of spin models by a feedback loop between a classical computer and a quantum co-processor, (Nature 569, 335 (2019)).
In the new setup, we created 2d-crystals with more than 100 ions. Structural configuration changes to metastable configurations are suppressed by fine-tuning the trap anisotropy. Preparation of the ion crystals at sub-mK temperatures is enabled by polarization-gradient cooling (NJP 22, 103013 (2020)) and EIT ground state cooling of the transverse motional modes (PRX Quantum 4, 040346 (2023)). For quantifying mode temperatures, a novel thermometry technique (PRX Quantum 4, 040346 (2023)) revealed motional heating rates of 0.5 phonons/s.
Qubits are encoded in the two Zeeman ground states of 40Ca+ ions. High-fidelity state measurements are achieved by electron shelving. Qubit manipulation is accomplished by a motion-sensitive Raman light field off-resonantly coupling the qubit states to P-states. Qubit coherence times >100 ms were found. An addressing unit has been developed for single-qubit control by differential light shifts. Raman beam are aligned by correlation spectroscopy (arXiv: 2203.12656). Long-range spin-spin interactions are realized by off-resonantly coupling all ions to all transverse modes using a bichromatic Raman interaction. In this way, we realized long-range Ising models for validating the performance of the simulator by comparing observed spin-spin correlations to exact simulations. Furthermore, we investigated non-equilibrium quantum dynamics by long-range XY models that generated spin squeezed states. Using the spin squeezing parameter as a benchmark, we demonstrated entanglement creation in 2d-crystals with >100 ions for which exact simulations are infeasible. We used a quantum-classical feedback loop for variationally optimizing the spin squeezing, obtaining up to 9.5 dB of noise reduction. Project results have been disseminated by scientific publications, talks at conferences and winter schools, and lab tours.
Since the project end, we improved the coherence of entangling operations by optimizing the Raman light fields. In a follow-up project from a national funding agency, we will replace the laser shelving the qubits to the metastable state by a more stable source for the realization of symmetric, informationally complete, positive operator-valued measures and shadow-tomography techniques. We also plan to integrate a high-power laser source for high-fidelity entanglement generation and alternative single-qubit control by strongly focused beams.
Picture of a 91-ion crystal imaged with the high-NA objective
Variational optimization of spin squeezing in an 91-ion crystal
Monolithic 3d ion trap for trapping of two-dimensional crystals
Photo of the monolithic trap wire-bonded to the chip carrier
Pictures of ions in different structural transitions with corresponding crystal lattice
Red sideband spectum of a 105-ion crystal after Doppler (red) and EIT (blue) cooling
Vacuum system and part of the optical setup
Quantum correlations in non-equilibrium Ising dynamics of a 19-ion crystal