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Measurement Back-Action and Photon Detection in Microwave Quantum Optics

Anton Frisk Kockum

Published Jan 1, 2012• 3 citations
OpenAlex

Abstract

In quantum optics, the interaction between atoms and photons is studied. In recent years, microwave quantum optics with superconducting circuits has emerged as an important tool for fundamental quantum optics experiments, and also as a promising way for implementing quantum computation. The main reason for this development is the ease with which strong coupling and other properties of artificial atoms and microwave photons can be engineered in such a setup. This thesis is comprised of two papers dealing with measurements in microwave quantum optics. In Paper I, we show how unwanted measurement back-action can be undone for certain measurements on one and two qubits dispersively coupled to a microwave resonator. An important application of this result is to improve parity measurements, which are integral to error-correction codes needed to implement large-scale quantum computing. In Paper II, we investigate the possibility of using a three-level artificial atom, a transmon, to mediate a cross-Kerr type interaction between photons. The idea is to use it as a single-photon detector in the microwave regime, a component currently missing in the experimentalist's toolbox. We show that there are fundamental limitations to this setup, resulting in an unsatisfactory signal-to-noise ratio.

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Typical photon counters involve absorption of photons to generate electric signals, thus basically destroying the information carried by the photon. This is all the more disastrous if the photon is used as a quantum information carrier, such as a part of an entangled pair. Quantum non-demolition (QND) measurements are de- signed to overcome this limitation. Such a non-destructive photon detection would play a key role in quantum networks where photons can be used as “flying” qubits.\nIn this thesis, using circuit QED we investigate if QND detection of a prop- agating microwave photon is possible. The system considered consists of a three level artificial atom (transmon) interacting with signal and probe fields. The fields are in the microwave regime with their frequencies on par with the energy levels of the transmon. The interaction of these two fields with the artificial atom, imparts a phase change on the probe field via the cross-Kerr effect. By measuring this phase change, we indirectly infer the presence of the signal.\nIn this thesis, we investigate if it is possible to achieve a single photon detection, at first using a single transmon and then using multiple transmons. We find that, while single photon detection is not possible with a single transmon, it is indeed possible with multiple transmons under certain conditions. We also find that with multiple transmons, we can have a large phase change in the probe, which might be desirable in other applications.

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I. Hoi

The realization of a quantum network composed of quantum nodes which process quantum fields and quantum channels to transfer quantum information has recently been proposed. In recent years, fundamental experiments produced by superconducting circuits suggest that they are promising candidates for realization of a quantum network. Superconducting circuit QED can act as quantum nodes, which can be linked by quantum channels, to transfer flying microwave photons (quantum information) from site to site on chip with high fidelity. Therefore, controlling the propagating microwave photons on chip is an essential step towards realization of a quantum network.In this thesis, we demonstrate a specific quantum node, namely the single photon router. The active element of the router is a single three-level artificial atom, a superconducting transmon type qubit, strongly coupled to a superconducting 1D transmission line. Strong coupling between the artificial atom and propagating microwave photons, revealed in high degree scattering of the resonance waves, has been observed. By exploiting the phenomenon of electromagnetically induced transparency (EIT), we can route a single photon signal from an input port to either of two output ports with an on-off ratio of approximately 90%. The switching time of the router is shown to be a few nanoseconds, consistent with theoretical expectations and the device parameters. Besides the router, we also observed some fundamental phenomenon of single atom, such as strong nonlinearity, anomalous dispersion and the Mollow Triplet.This thesis describes the motivation, theoretical background, design, implementation and the measurement results.

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In quantum optics, the interaction between atoms and photons is studied. In recent years, microwave quantum optics with superconducting circuits has emerged as an important tool for fundamental quantum optics experiments, and also as a promising way for implementing quantum computation. The main reason for this development is the ease with which strong coupling and other properties of artificial atoms and microwave photons can be engineered in such a setup.
This thesis is comprised of two papers dealing with measurements in microwave quantum optics. In Paper I, we show how unwanted measurement back-action can be undone for certain measurements on one and two qubits dispersively coupled to a microwave resonator. An important application of this result is to improve parity measurements, which are integral to error-correction codes needed to implement large-scale quantum computing.
In Paper II, we investigate the possibility of using a three-level artificial atom, a transmon, to mediate a cross-Kerr type interaction between photons. The idea is to use it as a single-photon detector in the microwave regime, a component currently missing in the experimentalist's toolbox. We show that there are fundamental limitations to this setup, resulting in an unsatisfactory signal-to-noise ratio.
Quantum optics in superconducting circuits, known as circuit QED, studies the interaction of photons at microwave frequencies with artificial atoms made of Josephson junctions. Although quite young, remarkable progress has been made in this field over the past decade, especially given the interest in building a quantum computer using superconducting circuits. In this thesis based on the appended papers, we look at generation, engineering and detection of microwave photons using superconducting circuits. We do this by taking advantage of the strong coupling, on-chip tunability and huge nonlinearity available in superconducting circuits. First, we present the strong photon-photon interaction measured experimentally, as shown in the giant cross-Kerr effect. In this work, conditional phase shift of about 20 degrees per photon was measured between two coherent fields at single photon level. Given this strong interaction, we propose and analyze a cascaded setup based on the cross-Kerr effect to detect itinerant microwave photons, a long outstanding problem with only recent experimental realizations. We show that a nondestructive detection of microwave photons is possible with few cascaded transmons. The on-chip tunability of Superconducting Quantum Interference Device (SQUID) is exploited to create a tunable superconducting resonator in the next presented experimental work. Finally, we show that by placing the atom at the end of a transmission line, microwave photons can be generated efficiently and on-demand. We also present a setup that can generate the photons in arbitrary wave packets.
Microwave quantum optics using superconducting circuits, also known as circuit QED, is a recent and promising field to study light-matter interactions at the fundamental level. In this field, artificial atoms made of superconducting elements interact with microwave photons routed through one dimensional transmission lines. This thesis is under the purview of circuit QED and is based on the three appended papers. In these three articles, we look at the problems of engineering photon-photon interaction (a la cross-Kerr effect) in microwaves using an artificial atom, storing and retrieving microwave photons using a tunable cavity and finally detecting a single propagating microwave photon non-destructively. The analysis is done using the framework of open quantum systems, where we use master equations and stochastic master equations to study the evolution of these artificial atoms in the presence of environment and under measurements respectively.
Detecting an itinerant microwave photon with high efficiency is an outstanding problem in quantum optics at microwave frequencies and in the fundamental quantum mechanics experimental toolbox. This subject has attracted a lot of attention and there are growing number of excellent experimental demonstrations and theoretical proposals towards this aim. However, due to the extremely low energy of microwave quanta, efficiently detecting a propagating microwave photon in a non-absorbing manner is still an unresolved challenge and it is the focus of the major part of this thesis. Motivated by a recent experiment that shows a superconducting artificial atom (a transmon) in a one-dimensional microwave transmission line exhibits gigantic cross-Kerr nonlinearities, 1000 times larger than in comparable optical systems, I investigate the possibility of detection single microwave photons using a transmon induced cross-Kerr-like interaction between two microwave fields. The photon number in one field is inferred through the measurement of the displacement of the other field. The first project on this subject is to investigate the feasibility of detecting a single microwave photon with signal-to-noise ratio (SNR) greater than unity using a three-level approximation for the transmon in an open transmission line, due to the saturation of transmon response to the probe intensity. After that, an improved scheme was proposed to overcome the limitations in the preceding work. By using a cavity probe field the signal photon induced probe displacement is strongly enhanced. Further additional transmon-cavity units can be cascaded to further improve the detection efficiency. It is shown that with only two transmons the distinguishability to resolve a single-photon state from the vacuum is up to 90%90\%90%. One advantage of this photon detection scheme is that it does not rely on the absorption of single microwave photons, which enables repeated measurements and further applications. Moreover, I also show how the measurement diminishes coherence in the photon number basis thereby illustrating a fundamental principle of quantum measurement: the higher the measurement efficiency, the greater is the decoherence. Apart from the investigation on the single microwave photon detection, this thesis also studies nonlinear dynamics of a hybrid coupled-resonator and opto-mechanical system. It is shown that the saddle-node bifurcation and the Hopf bifurcation appear in the system, which leads to bistability and limit cycle dynamics of the mechanical position and the output light intensity. More importantly, the opto-mechanical nonlinearity dramatically changes the transparency window of the coupled resonator induced transparency (CRIT) and based on the narrow and bistable CRIT transparency window, the proposed system is shown to be a good platform for the weak impulsive force detection with a good sensitivity.
We address recent advances in quantum optics with propagating microwaves\nin superconducting circuits. This research field exploits on the fact that the coupling between a superconducting artificial atom and propagating microwave photons in a one-dimensional (1D) open transmission line can be made strong enough to observe quantum effects, without using any cavity to confine the microwave photons.\nWe embed an artificial atom, a superconducting transmon qubit, in a 1D open\ntransmission line and investigate the scattering properties of coherent microwaves. When an input coherent state, with an average photon number much less than 1, is on resonance with the artificial atom, we observe extinction of up to 99% in the forward propagating field. We observe the strong nonlinearity of the artificial atom and under strong driving we observe the Mollow triplet. We also study the statistics of the reflected and transmitted beams, which are predicted to be nonclassical states. In particular, we demonstrate photon antibunching in the reflected beam by measuring the second-order correlation function. By applying a second control tone, we observe the Autler-Townes splitting and a giant cross-Kerr effect.\nFurthermore, we demonstrate fast operation of a single-photon router using\nthe Autler-Townes splitting. This device provides important steps towards the realization of a quantum network. This thesis describes the motivation, theoretical background, design, implementation and measurement results.
Typical photon counters involve absorption of photons to generate electric signals, thus basically destroying the information carried by the photon. This is all the more disastrous if the photon is used as a quantum information carrier, such as a part of an entangled pair. Quantum non-demolition (QND) measurements are de- signed to overcome this limitation. Such a non-destructive photon detection would play a key role in quantum networks where photons can be used as “flying” qubits.\nIn this thesis, using circuit QED we investigate if QND detection of a prop- agating microwave photon is possible. The system considered consists of a three level artificial atom (transmon) interacting with signal and probe fields. The fields are in the microwave regime with their frequencies on par with the energy levels of the transmon. The interaction of these two fields with the artificial atom, imparts a phase change on the probe field via the cross-Kerr effect. By measuring this phase change, we indirectly infer the presence of the signal.\nIn this thesis, we investigate if it is possible to achieve a single photon detection, at first using a single transmon and then using multiple transmons. We find that, while single photon detection is not possible with a single transmon, it is indeed possible with multiple transmons under certain conditions. We also find that with multiple transmons, we can have a large phase change in the probe, which might be desirable in other applications.
The realization of a quantum network composed of quantum nodes which process quantum fields and quantum channels to transfer quantum information has recently been proposed. In recent years, fundamental experiments produced by superconducting circuits suggest that they are promising candidates for realization of a quantum network. Superconducting circuit QED can act as quantum nodes, which can be linked by quantum channels, to transfer flying microwave photons (quantum information) from site to site on chip with high fidelity. Therefore, controlling the propagating microwave photons on chip is an essential step towards realization of a quantum network.In this thesis, we demonstrate a specific quantum node, namely the single photon router. The active element of the router is a single three-level artificial atom, a superconducting transmon type qubit, strongly coupled to a superconducting 1D transmission line. Strong coupling between the artificial atom and propagating microwave photons, revealed in high degree scattering of the resonance waves, has been observed. By exploiting the phenomenon of electromagnetically induced transparency (EIT), we can route a single photon signal from an input port to either of two output ports with an on-off ratio of approximately 90%. The switching time of the router is shown to be a few nanoseconds, consistent with theoretical expectations and the device parameters. Besides the router, we also observed some fundamental phenomenon of single atom, such as strong nonlinearity, anomalous dispersion and the Mollow Triplet.This thesis describes the motivation, theoretical background, design, implementation and the measurement results.