Sisyphus cooling and amplification by a superconducting qubit

Abstract

Laser cooling of the atomic motion paved the way for remarkable achievements in the fields of quantum optics and atomic physics, including Bose-Einstein condensation and the trapping of atoms in optical lattices. More recently superconducting qubits were shown to act as artificial two-level atoms, displaying Rabi oscillations, Ramsey fringes, and further quantum effects 1,2,3 . Coupling such qubits to resonators 4,5,6,7 brought the superconducting circuits into the realm of quantum electrodynamics (circuit QED). It opened the perspective to use superconducting qubits as micro-coolers or to create a population inversion in the qubit to induce lasing behavior of the resonator 8,9,10,11 . Furthering these analogies between quantum optical and superconducting systems we demonstrate here Sisyphus cooling 12 of a low frequency LC oscillator coupled to a near-resonantly driven superconducting qubit. In the quantum optics setup the mechanical degrees of freedom of an atom are cooled by laser driving the atom's electronic degrees of freedom. Here the roles of the two degrees of freedom are played by the LC circuit and the qubit's levels, respectively. We also demonstrate the counterpart of the Sisyphus cooling, namely Sisyphus amplification.For red-detuned high-frequency driving of the qubit the low-frequency LC circuit performs work in the forward and backward part of the oscillation cycle, always pushing the qubit up in energy, similar to Sisyphus who always had to roll a stone uphill. The oscillation cycle is completed with a relaxation process, when the work performed by the oscillator together with a quantum of energy of the high-frequency driving is released by the qubit to the environment via spontaneous emission. For blue-detuning the same mechanism creates excitations in the LC circuit with a tendency towards lasing and the characteristic line-width narrowing. In this regime "lucky Sisyphus" always rolls the stone downhill. Parallel to the experimental demonstration we analyze the system theoretically and find quantitative agreement, which supports the interpretation and allows us to estimate system parameters.The system considered is shown in the inset of Fig. 1. It consists of a three-junction flux qubit 13 , with the two qubit FIG. 1: (a) The energy levels of the qubit as a function of the energy bias of the qubit ε(fx) = 2Φ0Ipfx. The sinusoidal current in the tank coil, indicated by the wavy line, drives the bias of the qubit. The starting point of the cooling (heating) cycles is denoted by blue (red) dots. The resonant excitation of the qubit due to the high-frequency driving, characterized by ΩR0, is indicated by two green arrows and by the Lorentzian depicting the width of this resonance. The relaxation of the qubit is denoted by the black dashed arrows. The inset shows a schematic of the qubit coupled to an LC circuit. The high frequency driving is provided by an on-chip microwave antenna. (b) SEM picture of the superconducting flux qubit prepared by shadow evaporation technique.

Vibronic Spectroscopy of an Artificial Molecule

“…(ii) The second effect is a damping or amplification effect that is similar to resolved-sideband cooling in optics [12]. The same effect has been discussed also in Josephson qubits [30] and has been seen for the first vibronic transitions [22]. Consider the lower sideband fringes in Fig.…”

“…A large number of experiments could be interpreted using the molecular analogy, including qubits coupled to oscillators [13][14][15][16][17][18][19][20][21][22] and qubits driven by an intense field [23][24][25][26][27]. The analogy is particularly apt for our case because there is clear separation of the electronic and vibrational energy scales, we drive at two frequencies, and the parameters of the molecule can be tuned in a wide range.…”

Single-qubit lasing in the strong-coupling regime

“…In these "circuit QED" setups a superconducting qubit plays the role of an artificial atom, while the radiation field is replaced by the modes of an electric resonator. In some of these experiments a strong enhancement of the resonator field and lasing were observed [14,15].…”

Implementation of an Impedance-MatchedΛSystem by Dressed-State Engineering

“…We can also make the potential asymmetric, for example by introducing flux bias in flux qubits. The lowest three levels then function as a Λ system, which have been used to demonstrate, for example, lasing and cooling of qubits [17][18][19]. However, it is difficult to satisfy the impedance-matching condition, i.e., identical decay rates from the second excited state, in the Λ systems thus created.…”