Superconducting quantum circuits exhibit an extraordinary potential for future electronic applications. The most important element in superconducting quantum circuits is the Josephson junction, built by nanofabricated superconducting electrodes separated by a thin insulating layer. Superconducting devices allow mixing and parametric amplification up to the terahertz range under low energy consumption and ultra-low noise. High frequency signals at low temperatures exhibit a photon energy exceeding the thermal energy, resulting in the need of a quantum mechanical treatment of the electromagnetic field at millimeter-wave frequencies. In this work, we investigate the dynamic behaviour of a negative-resistance, dissipative DC biased Josephson parametric amplifier. The Langevin theory is used for modeling of the dissipation in the resonant circuits. We investigate Markovian dynamics for modeling the dissipative Josephson parametric amplifier in a correct manner, neglecting memory effects. We derive the equations of motions of the resonator operators and numerically evaluate the time evolution of the signal and noise energies. Applying a phenomenological multi-photon coupling approach, a correction of the Markovian assumption is achieved providing an expected saturation in the dynamical behaviour of the circuit.
Superconducting quantum circuits exhibit an extraordinary potential for future electronic applications. The most important element in superconducting quantum circuits is the Josephson junction, built by nanofabricated superconducting electrodes separated by a thin insulating layer. Superconducting devices allow mixing and parametric amplification up to the terahertz range under low energy consumption and ultra-low noise. High frequency signals at low temperatures exhibit a photon energy exceeding the thermal energy, resulting in the need of a quantum mechanical treatment of the electromagnetic field at millimeter-wave frequencies. In this work, we investigate the dynamic behaviour of a negative-resistance, dissipative DC biased Josephson parametric amplifier. The Langevin theory is used for modeling of the dissipation in the resonant circuits. We investigate Markovian dynamics for modeling the dissipative Josephson parametric amplifier in a correct manner, neglecting memory effects. We derive the equations of motions of the resonator operators and numerically evaluate the time evolution of the signal and noise energies. Applying a phenomenological multi-photon coupling approach, a correction of the Markovian assumption is achieved providing an expected saturation in the dynamical behaviour of the circuit.
Abstract. In this work, we derive the dynamics of the lossy DC pumped non-degenerate Josephson parametric amplifier (DCPJPA). The main element in a DCPJPA is the superconducting Josephson junction. The DC bias generates the AC Josephson current varying the nonlinear inductance of the junction. By this way the Josephson junction acts as the pump oscillator as well as the time varying reactance of the parametric amplifier. In quantum-limited amplification, losses and noise have an increased impact on the characteristics of an amplifier. We outline the classical model of the lossy DCPJPA and derive the available noise power spectral densities. A classical treatment is not capable of including properties like spontaneous emission which is mandatory in case of amplification at the quantum limit. Thus, we derive a quantum mechanical model of the lossy DCPJPA. Thermal losses are modeled by the quantum Langevin approach, by coupling the quantized system to a photon heat bath in thermodynamic equilibrium. The mode occupation in the bath follows the Bose-Einstein statistics. Based on the second quantization formalism, we derive the Heisenberg equations of motion of both resonator modes. We assume the dynamics of the system to follow the Markovian approximation, i.e. the system only depends on its actual state and is memory-free. We explicitly compute the time evolution of the contributions to the signal mode energy and give numeric examples based on different damping and coupling constants. Our analytic results show, that this model is capable of including thermal noise into the description of the DC pumped non-degenerate Josephson parametric amplifier.
With a large portfolio of elemental quantum components, superconducting quantum circuits have contributed to dramatic advances in microwave quantum optics. Of these elements, quantum-limited parametric amplifiers have proven to be essential for low noise readout of quantum systems whose energy range is intrinsically low (tens of µeV). They are also used to generate non classical states of light that can be a resource for quantum enhanced detection. Superconducting parametric amplifiers, like quantum bits, typically utilize a Josephson junction as a source of magnetically tunable and dissipation-free nonlinearity. The magnetic control is not an industry standard for devices and starts already to be an issue in large scale circuits. In recent years, efforts have been made to introduce semiconductor weak links as electrically tunable nonlinear elements, with demonstrations of microwave resonators and quantum bits using semiconductor nanowires, a two dimensional electron gas, carbon nanotubes and graphene. However, given the challenge of balancing nonlinearity, dissipation, participation, and energy scale, parametric amplifiers have not yet been implemented with a semiconductor weak link. The work presented in this PhD thesis demonstrates the design, fabrication and performances of a parametric amplifier leveraging a graphene Josephson junction.The graphene is encapsulated in between hBN flakes in order to improve its quality. Using such high quality junctions, we demonstrate amplification with 20 dB gain which is the milestone for overcoming noise of the classical amplifiers in the rest of the amplification chain. The Josephson parametric amplifier being based on a resonant structure (around 6 GHz) suffers from the gain bandwidth product limiting the amplification to a few MegaHertz frequency range. The use of a side gate to electrically tune the graphene gives control of the Josephson junction inductance and thus the resonant frequency of the amplifier. We demonstrate a near 1 GHz tunability of the amplification frequency with the use of a side gate which is as good as the tunability offered by using a magnetic flux on a SQUID for similar amplifier designs. Moreover, graphene has shown to exhibit nonlinear loss under a strong microwave irradiation arising because of dynamics in the Andreev states. Dissipation is known to add intrinsic noise on quantum amplifiers and could be a problem for quantum limited parametric amplification. We demonstrate that despite the presence of nonlinear loss, graphene based Josephson parametric amplifiers can reach near quantum limited amplification. A two photon loss model was used to describe the behaviour of the device but we show that a more complex model is required in order to take into account the nonlinear dissipation and the non-sinusoidal current phase relation. We also studied the dynamic range and showed that the graphene based Josephson parametric amplifier can reach a 1 dB compression point of -123 dBm which is as good as single tunnel junctions based parametric amplifiers. Our results expand the toolset for electrically tunable superconducting quantum circuits and offer new opportunities for the development of quantum technologies such as quantum computing, quantum sensing and fundamental science.
In circuit quantum electrodynamical systems, the quasiparticle-related losses in Josephson junctions are suppressed due to the gap in the superconducting density of states which is much higher than the typical energy of a microwave photon. In this work, we show that a strong drive even at a frequency lower than twice the superconductor gap parameter can activate dissipation in the junctions due to photon-assisted breaking of the Cooper pairs. Both the decay rate and noise strength associated with the losses are sensitive to the dc phase bias of the junction and can be tuned in a broad range by the amplitude and the frequency of the external driving field, making the suggested mechanism potentially attractive for designing tunable dissipative elements. We also predict pronounced memory effects in the driven Josephson junctions, which are appealing for both theoretical and experimental studies of non-Markovian physics in superconducting quantum circuits. We illustrate our theoretical findings by studying the spectral properties and the steady-state population of a low-impedance resonator coupled to the driven Josephson junction: we show the emergence of non-Lorentzian spectral lines and broad tunability of effective temperature of the steady state.
Union Radio-Scientifique Internationale
International Union of Radio Science
U.R.S.I. Landesausschuss in der Bundesrepublik Deutschland e.V.
Kleinheubacher Tagung 2013
Miltenberg
•
Germany
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23. -
25. Septembe
r
U.R.S.I. Landesausschuss in der Bundesrepublik Deutschland e.V.
Kleinheubacher Tagung 2016
Miltenberg
•
Germany
•
26. – 28. September 2016
14:10 – 14:30 Uhr:
KH2016-D-10
Waldemar Kaiser, Michael Haider, Johannes Russer, Peter H. Russer, Christian Jirauschek
(Technische Universitat Munchen, Germany)
Modeling of the lossy Josephson parametric amplifier
Recent advances in superconducting nanoelectr
onic circuits exhibit the potential for future
electronic
applications. Experimental and theoretical research
on superconducting quantum circuits based on the
Josephson effect have recently gained more and
more attention due to developments in quantum
information theory and quantum metrology (Russe
r and Russer, 2011). The Josephson effect is
observed, if two superconducting materials ar
e weakly coupled across a tunnel barrier or
a narrow conducting bridge. Electronic devices based on the Josephson effect allow the generation,
detection, mixing and parametric amplification of hi
gh-frequency signals. Mor
eover, Josephson devices
are nanometre-sized low power devices and show hi
gh sensitivity. So far, Josephson parametric
amplifiers have been treated classically as well
as quantum mechanically. The existing quantum
mechanical models do not include loss contributions (Russer and Russer, 2012).
In this work the lossy negative-
resistance Josephson parametric am
plifier is analyzed. Losses are
considered using the quantum Langevin method. Hereby
, the resonator circuits, i.e. the signal and the
idler circuit, are coupled to a heat bath, represented
by a photon gas in thermal equilibrium. In this way,
also temperature dependencies are taken into account. In our model, the heat bath consists of harmonic
oscillators, inducing fluctuations in the resonators a
nd causing damping of the signal energy (Jirauschek
and Russer, 2012). The DC biased Josephson junction is causing a strong interaction between the idler
and the signal modes. Thus, power exchange occurs
between the signal and the idler mode, as well as
between the DC power supply and the resonator ci
rcuits. The energy conversion in the DC-pumped
Josephson parametric amplifier follows the Manley-Row
e equations, with an additional DC term (Russer,
1971).
The time evolution of the signal e
nergy and the noise contributions ar
e derived based on the Heisenberg
equations of motion. The rotating wave approximati
on is applied in order to simplify the Josephson
coupling Hamiltonian.We assume the heat bath noise cont
ributions to follow the statistics of a Markovian
process. We have explicitly computed the time evolut
ion of the various energy contributions for different
initial settings. The signal photon number in therma
l equilibrium is determined by the photon occupation
number of the heat bath, given by
Boltzmann statistics, and the damping constants. Our analytic results
show, that this model is capable of including th
ermal noise into the description of the Josephson
parametric amplifier. For low damping constants, the
signal energy is amplified exponentially as shown in
previous publications without loss considerations (Russer and Russer, 2012).
In this paper, we are constructing a circuit quantum electrodynamic model describing dissipative effects in a Josephson traveling-wave parametric amplifier (JTWPA). Losses and noise are treated using the quantum Langevin method. The total Hamiltonian of our model describes the coupling of the modes in a parametric four-wave-mixing scheme, as well as the interaction with the environment. Based on the Heisenberg equations of motion, we obtain the temporal evolution of the signal photon number and analyze the signal gain of the JTWPA.