Electron Spin Resonance at the Single Atom Level

Summary

Electron spin resonance (ESR) holds the power to manipulate quantum states with exquisite precision. The technique relies on providing an oscillating magnetic field to drive transitions between quantum states. This technique has historically been used to study materials in which a strong magnetic field splits certain quantum states into two different energy levels. The difference between two energy levels can be described by a frequency. When this frequency is matched with the oscillating magnetic field, a transition between states occurs, which is measurable and can be used to further understand the material. While this approach was originally used to study the structure of materials, more recently, the nascent field of quantum computing uses this same principle. In this case, the idea is not to simply induce a transition, but to stop the transition halfway between both states. This results in a quantum superposition: a combination of both states existing at once. This may be exploited to perform calculations using both energy states at the same time. Doing this on so-called qubits (quantum bits) requires very fine control of the quantum states, which is currently one of the main bottlenecks towards scaling up this revolutionary technology towards commercial use. Globally, there are various qubit systems being explored right now, such as superconducting qubits and trapped ion qubits, among others. In our nanoelectronics lab, we study a variety of qubits from single atoms to superconducting Josephson junctions to gain an understanding of their fundamental properties and limitations from environmental factors. 

Description

To study electron spin resonance (ESR) on single atoms requires a tool that can probe at atomic length scales. The scanning tunneling microscope (STM) is ideally suited for this, using a tunneling current to probe surfaces. To implement this ESR-STM combination, we send a radio frequency (RF, typically 5-25 GHz) oscillating voltage to the tip-sample junction, resulting in an oscillating electric field. With a magnetic tip, typically made by picking up a couple of magnetic atoms like iron, we turn this into an oscillating magnetic field. With this, we can controllably bring a single atom into a higher energy state (an excited state). With the right magnetic tip, this will even result in a different current, which allows us to confirm this excitation. However, this process is typically very fast, in the order of nanoseconds to microseconds. For such experiments, the STM typically operates at such low currents (≈ 1 to 10 pA) that a current amplifier is used, which unfortunately is often blind to signals faster than a millisecond. To overcome the limitation of the slow transimpedance amplifier, we use lock-in techniques, modulating the RF power to the STM junction. 

Such an experiment has many technical requirements. For example, we need proper vibration isolation to maintain a stable tip-sample distance. We also require a cryogenic environment (< 4 K) where such quantum behavior is observable. We need high-quality lines for the RF signals, which should have good transmission characteristics but not have much heat loss at ultra-low temperatures. These requirements, among many others, make such systems challenging to master. Here at NIST, we have designed and constructed a measurement lab for the most stable environment to provide optimal control of these qubit systems, with an ESR-STM that can operate down to ≈10 mK and with four dedicated RF lines controllable through cryogenic switches. Beyond ESR-STM, our system has exchangeable scanning modules, allowing us to swap to other measuring techniques such as atomic force microscopy (AFM) and transport measurements, and to explore their integration with ESR. 

With this state-of-the-art instrument, we are working on: (1) demonstrating entanglement between atoms, (2) studying the various sources of decoherence on qubit systems (i.e., how consistent a qubit can stay in its quantum superposition), and (3) exploring novel techniques to further enhance qubit stability.  

Demonstration of Entanglement 

Fig. 1. [Top Left] Experimental set-up of entanglement eavesdrop experiment. Three titanium atoms are placed on an MgO surface atop of silver(100). These atoms express themselves as spin-1/2 and are coupled together through some coupling strength J₁ and J₂. With either the magnetic tip or a nearby magnetic iron atoms these can be coherently excited. The sensor atom (S) maps the excitations of atoms A (for Alice) and B (for Bob), without destroying the entanglement between them. Right diagram shows the energy levels of this system. [Bottom] Nine illustrations describing possible causes of decoherence to atomic quantum systems measured by a scanning probe. See text for more detail. [Top Right] Energy diagram and Bloch sphere of two quantum states described as either pure N_A and N_B or as a symmetric (+) or antisymmetric (-) superposition of these states. At a particular value for transverse magnetic field Bx, called a diabolic point, lifetime (T₁) will increase due to de-hybridization. An open question remains what will happen to the decoherence time (T₂) and the Rabi flop rate (Ω). 

Credit: NIST

For quantum information applications, two people, Alice and Bob, are often imagined wanting to relay a message between each other, without anyone listening in. One way to make sure no one listens in is by making use of entanglement, a feature of quantum physics where two objects share certain properties. Entanglement between photons (packets of light) is nowadays easily achieved. Entanglement between larger objects like atoms is more elusive. In fact, many experiments that aim to prove such entanglement are too invasive and break the entanglement in the process. To overcome this, we perform our measurement on a sensor atom that is eavesdropping on two entangled atoms, Alice and Bob.  

Enhancing Qubit Stability 

To perform such experiments, this platform requires extreme stability, as there are many sources of decoherence for both the entangled system, and any quantum-coherent system in scanning probe microscopy. Better understanding such sources helps us design better systems for the booming quantum technology industry. Such sources include incoming radio frequency radiation, bath electrons interacting with the object of interest, thermal noise, fluctuations in nuclear magnetic moments, mechanical instability, tunneling electrons, ground loops and/or phonons. 

Investigating Decoherence 

Besides improving equipment, one may also exploit unique quantum phenomena to enhance coherence. For example, by adjusting an external magnetic field, the extent to which the two states are in a superposition can be adjusted. At a particular point, called a diabolic point, a de-hybridized state emerges, whose lifetime (T₁) would be orders of magnitude larger. What we don’t yet know is how this de-hybridization affects both the coherence time (T₂) and the speed (Ω) at which the state can be controlled. Ideally, these would change at different rates with respect to the external field, which would give additional control parameters for future quantum technology.