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Simulating 2d Spin Lattices with Ion Crystals

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

Reporting period: 2019-03-01 to 2020-08-31

At the level of the individual constituents of matter, the behaviour 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 even on supercomputers for systems containing even 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, like for example phases of matter that arise in quantum mechanics or high-temperature superconductivity, 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. It has been shown that important optimization problems, which might arise in an industrial context, can be mapped to the dynamics of many-particle problems.
Within this project, we aim to develop trapped-ion based quantum simulations to larger numbers of particles by developing an experimental apparatus capable of manipulating two-dimensional ion crystals containing 50-100 particles with quantum control over each individual ion. The approach pursued in this project 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 when exciting the ions with laser light. This approach necessitates the development of a new ion trap apparatus and of novel technique for manipulating the ions. The device will be 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.
A novel microfabricated ion trap designed for carrying out quantum simulations with two-dimensional ion crystals constitutes the centerpiece of the new setup.
Based on computer simulations, we designed a novel monolithic 3D linear Paul trap (Fig. 1) that was fabricated by the company Translume using subtractive 3d printing, a laser-assisted structuring technique for glass substrates, which can be subsequently metallized for defining the trap electrodes. This approach enabled the construction of a monolithic trap that overcomes the difficulty of precise alignment of multiple 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. On the technical side, the laser-written trap wafer was designed to enable metallization of the trap without the need of using masks for defining the different electrodes.
For housing the ion trap, we developed and built a new compact vacuum chamber (Fig. 2a) that provides good optical access to trapped ion crystals. Additionally, the vacuum chamber was designed to achieve an excellent ultra-high vacuum by using a geometry enabling large pumping rates and using a vacuum chamber featuring low outgassing rates. At the same time, all laser sources needed for manipulating the ions were purchased and installed and all optical setups (a part is shown in Fig.2b) needed for addressing the ions by laser pulses with precisely controlled timing, frequency, intensity and polarization were installed. For coherent excitation of the ions, the laser pulse properties are controlled by a novel versatile radiofrequency source that is integrated into an experiment control program steering the experimental apparatus and recording measurements on the ions.
In a parallel to setting up this new machine, experiments were carried out in an existing apparatus. In one line of research, random measurements were used to measure purities and entanglement properties of strings with up to 20 ions (Science 364, 260 (2019)), demonstrating a cross-platform verification protocol (PRL 124, 010504 (2020)) and measuring quantum information scrambling in a trapped-ion quantum simulator (arXiv:2001.02176). Secondly, we demonstrated variational simulation of spin models using a feedback loop between a classical computer and a quantum co-processor, while benefiting from quantum resources consisting of a 20-ion string (Nature 569, 335 (2019)). Thirdly, we created slightly two-dimensional ion crystals of up to 22 ions, demonstrated sub-Doppler cooling in a polarization gradient and investigated the coherence of some of the ions’ collective vibrational modes. Additionally, efficient methods for quantum state detection of 2d-ion crystals were developed.
The project has yielded results going beyond state-of-the-art in the following ways:
The analysis of complex multi-qubit entangled states by random measurements enables an agnostic analysis of state properties that is more efficient than the traditional approach based on quantum state tomography.
The experiments on variational quantum simulation demonstrate the potential of analog quantum simulations for the investigation of quantum models beyond the ones that can be directly realized in the experimental setup.
The development of a monolithic three-dimensional segmented trap provides a versatile tool for trapping multi-ion crystals that is also of interest for trapped-ion precision measurements. The realization of polarization gradient cooling of large ion crystals demonstrates a cooling technique that is easy to implement, offers fast cooling rates and enables sub-Doppler cooling of vibrational modes over a fairly large frequency range. Finally, the cooling of two-dimensional zig-zag crystals to low temperatures and the observation that the cooled crystals stay cold over tens of milliseconds constitute a first step demonstrating the preparation of 2D crystals at low temperatures.
Till the end of the project, we expect to have an experimental apparatus with single-qubit control at our disposition that is capable of creating complex entangled states of 50-100 qubits whose properties can no longer be exactly simulated using numerical methods.