## Periodic Reporting for period 1 - XmonMASER (Josephson maser and heat transport in dissipative open quantum systems)

Reporting period: 2019-05-01 to 2021-04-30

In recent years circuit quantum electrodynamics (QED) platforms consisting of a superconducting quantum interference device (SQUID) coupled to resonators were exploited to study quantum thermodynamics and heat transport, with potential to realize quantum thermal machines. Such quantum systems have recommended as objects to study the fundamental quantum properties and more interestingly were proposed for quantum information processing platforms.

The fundamental knowledge of quantum physics can be immediately applicable in both the microelectronics industry, and communication sectors, and it will have a great impact on society both in Europe and globally. In particular, it can help to understand quantum effects and solve dissipation problems in large-scale quantum computers. Accurate quantum computing will usher in a revolution in many fields such as chemistry, drug-design, and meteorology, which require simulation of complex multivariable, high dimensional systems.

The main scientific and technological goals are: to study the effect of anharmonicity in the heat transport in a dissipative open quantum system; and to realise a Josephson maser, to demonstrate a coherent emission of microwave photons driving by a single ‘artificial atom’ - a superconducting qubit.

The fundamental knowledge of quantum physics can be immediately applicable in both the microelectronics industry, and communication sectors, and it will have a great impact on society both in Europe and globally. In particular, it can help to understand quantum effects and solve dissipation problems in large-scale quantum computers. Accurate quantum computing will usher in a revolution in many fields such as chemistry, drug-design, and meteorology, which require simulation of complex multivariable, high dimensional systems.

The main scientific and technological goals are: to study the effect of anharmonicity in the heat transport in a dissipative open quantum system; and to realise a Josephson maser, to demonstrate a coherent emission of microwave photons driving by a single ‘artificial atom’ - a superconducting qubit.

The first objective of this project is an investigation on qubit-mediated heat transport between two mesoscopic thermal reservoirs. In this implementation, thermal reservoirs consist in microfabricated normal-metal resistors acting as dissipative terminations to two different quarterwave microwave resonators. The mesoscopic resistors are designed for fast thermalization, linking the photonic population of each resonator to the electron temperature of the corresponding reservoir. The controllable element is a transmon type qubit, capacitively coupled between the two resonators. We present heat transport study in such system consisting of a transmon type qubit coupled via two unequal filters to two similar ohmic resistors. We focus on the rectification of the heat transport between thermal reservoirs and the effect of anharmonicity controlled by the qubit. Our results show that the transport coefficient in the resonator-qubit-resonator system is highly sensitive to the temperatures of the qubit and reservoirs. This work is published in the open access Communications Physics 3, 40 (2020).

The subject of the second objective is to realise a Josephson maser. We developed a theoretical model of an on-chip three level maser using single artificial atom in a superconducting circuit. The pumping and the idler transition are enabled by a thermal bias in a flux qutrit, where transitions between ground and the second excited states are made possible by using a specific geometry of Josephson junctions. By flux biasing the qutrit we tilt the double-well potential and we enhance the anharmonicity. The output power is estimated using a mesoscopic metallic resistor which acts as a bath. The direction of power through flux qutrit is independent of the temperature of this detector bath which is a necessary condition for population inversion. This opens up an effective way to measure population inversion in superconducting qubits. The population inversion is maintained in the lowest two states while finite power output is obtained. We discuss the condition for the lasing by connecting the output resonator to a transmission line. We estimate the power in terms of tunable circuit parameters. We observe Poissonian photon number distribution in the output resonator for sufficiently large temperature bias. The proposed method of on-chip conversion of heat into microwave radiation and control of energy-level populations by heating provide additional useful tools for circuit quantum electrodynamics experiments. This work is published in Phys. Rev. B 102, 104503 (2020).

Next, we investigate the qubit-mediated heat currents between three thermal baths. In this context, we present the realization of a three terminal system containing an artificial atom connected to three resonators terminated by mesoscopic resistors. In this implementation, the qubit is coupled to three unequal halfwave microwave resonators, which frequencies are designed to couple thermal baths to particular interlevel qubit transitions. The coplanar waveguide resonators are further coupled to microfabricated normal-metal resistors. The resistors having fast thermalization, allow the electron temperature control to reach the desired photonic population of each resonator, as well as the temperature readout. By heating one of the resistors and monitoring the temperatures of the other two, we determine photonic heat currents in the system. Adjusting the transitions of the flux-type qubit, capacitively coupled between the resonators, we demonstrate tunability of the effective magnitude of photon-mediated thermal conductance at the level of 1 aW. By comparing to the microwave transmission measurements, we demonstrate clear correlation between the level splitting of the qubit and the heat currents flowing through it. This work is submitted to Nature Communications.

The results of this project were presented at conferences:

1) “Control of photonic heat transport in superconducting circuits”, Conference on Quantum ThermoDynamics, QTD 2020, online, 2020.

2) Quantum thermodynamics in non-equilibrium systems, QTDNEQ20, online, 2020.

3) “Rectification of photonic heat current”, New Trends in Quantum Light and Nanophysics, QLIN-2019, Acquafredda, Italy, 2019.

4) Quantum ThermoDynamics conference, QTD2019, Finland, 2019.

The subject of the second objective is to realise a Josephson maser. We developed a theoretical model of an on-chip three level maser using single artificial atom in a superconducting circuit. The pumping and the idler transition are enabled by a thermal bias in a flux qutrit, where transitions between ground and the second excited states are made possible by using a specific geometry of Josephson junctions. By flux biasing the qutrit we tilt the double-well potential and we enhance the anharmonicity. The output power is estimated using a mesoscopic metallic resistor which acts as a bath. The direction of power through flux qutrit is independent of the temperature of this detector bath which is a necessary condition for population inversion. This opens up an effective way to measure population inversion in superconducting qubits. The population inversion is maintained in the lowest two states while finite power output is obtained. We discuss the condition for the lasing by connecting the output resonator to a transmission line. We estimate the power in terms of tunable circuit parameters. We observe Poissonian photon number distribution in the output resonator for sufficiently large temperature bias. The proposed method of on-chip conversion of heat into microwave radiation and control of energy-level populations by heating provide additional useful tools for circuit quantum electrodynamics experiments. This work is published in Phys. Rev. B 102, 104503 (2020).

Next, we investigate the qubit-mediated heat currents between three thermal baths. In this context, we present the realization of a three terminal system containing an artificial atom connected to three resonators terminated by mesoscopic resistors. In this implementation, the qubit is coupled to three unequal halfwave microwave resonators, which frequencies are designed to couple thermal baths to particular interlevel qubit transitions. The coplanar waveguide resonators are further coupled to microfabricated normal-metal resistors. The resistors having fast thermalization, allow the electron temperature control to reach the desired photonic population of each resonator, as well as the temperature readout. By heating one of the resistors and monitoring the temperatures of the other two, we determine photonic heat currents in the system. Adjusting the transitions of the flux-type qubit, capacitively coupled between the resonators, we demonstrate tunability of the effective magnitude of photon-mediated thermal conductance at the level of 1 aW. By comparing to the microwave transmission measurements, we demonstrate clear correlation between the level splitting of the qubit and the heat currents flowing through it. This work is submitted to Nature Communications.

The results of this project were presented at conferences:

1) “Control of photonic heat transport in superconducting circuits”, Conference on Quantum ThermoDynamics, QTD 2020, online, 2020.

2) Quantum thermodynamics in non-equilibrium systems, QTDNEQ20, online, 2020.

3) “Rectification of photonic heat current”, New Trends in Quantum Light and Nanophysics, QLIN-2019, Acquafredda, Italy, 2019.

4) Quantum ThermoDynamics conference, QTD2019, Finland, 2019.

In this project we have designed, fabricated and characterized superconducting circuits containing resonator-qubit-resonator assembly with embedded capacitors and terminating ohmic resistors. The investigated circuits appear to be a promising platform for studying heat transport via superconducting qubits in the quantum limit and to realize quantum circuits for thermodynamics experiments.

We have developed a wireless quantum heat rectifier, the thermal counterpart to the electronic diode, which demonstrates a flux-tunable photonic heat rectification up-to 12.5%. This device is integratable with superconducting circuits, as a means of exploring the frontiers of quantum thermodynamics and heat transport manipulation in superconducting devices.

We have constructed a model of thermally operated on-chip three level maser in a superconducting circuit which converts heat into a coherent source of photons. We show an experimentally feasible technique to detect population inversion in artificial atom. Other than the usefulness of masers in its own right, possible applications of our model include efficient thermal management and a way to construct a coherent source of photons in quantum circuits. We have studied the heat transport by photons in a three terminal system containing a flux qubit realized as superconducting loop with three identical Josephson junctions. The work presented here paves the way towards practical realization of an on-chip superconducting quantum circuits with qubits coupled to multiple resonators: quantum heat transistors, thermal amplifiers and heat pumped masers.

We have developed a wireless quantum heat rectifier, the thermal counterpart to the electronic diode, which demonstrates a flux-tunable photonic heat rectification up-to 12.5%. This device is integratable with superconducting circuits, as a means of exploring the frontiers of quantum thermodynamics and heat transport manipulation in superconducting devices.

We have constructed a model of thermally operated on-chip three level maser in a superconducting circuit which converts heat into a coherent source of photons. We show an experimentally feasible technique to detect population inversion in artificial atom. Other than the usefulness of masers in its own right, possible applications of our model include efficient thermal management and a way to construct a coherent source of photons in quantum circuits. We have studied the heat transport by photons in a three terminal system containing a flux qubit realized as superconducting loop with three identical Josephson junctions. The work presented here paves the way towards practical realization of an on-chip superconducting quantum circuits with qubits coupled to multiple resonators: quantum heat transistors, thermal amplifiers and heat pumped masers.