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arXiv:1010.5960 · Physical Review Letters

Proposal for an Optical Laser Producing Light at Half the Josephson Frequency

Frans Godschalk, Fabian Hassler, Yuli V. Nazarov

Published Aug 9, 2011• 28 citations
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Abstract

We describe a superconducting device capable of producing laser light in the visible range at half of the Josephson generation frequency with the optical phase of the light locked to the superconducting phase difference. It consists of two single-level quantum dots embedded in a p-n semiconducting heterostructure and surrounded by a cavity supporting a resonant optical mode. We study decoherence and spontaneous switching in the device.

DOI
10.1103/physrevlett.107.073901

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We describe a superconducting device capable of producing laser light in the visible range at half of the Josephson generation frequency with the optical phase of the light locked to the superconducting phase difference. It consists of two single-level quantum dots embedded in a p-n semiconducting heterostructure and surrounded by a cavity supporting a resonant optical mode. We study decoherence and spontaneous switching in the device.
We describe a superconducting device capable of producing laser light in the visible range at half the Josephson generation frequency, with the optical phase of the light locked to the superconducting phase difference. An earlier proposed device, the so-called ``half-Josephson laser'' [Phys. Rev. Lett. 107, 073901 (2011)], cannot provide long coherence times, because of spontaneous switchings between the emitter states. To circumvent this we consider $N\ensuremath{\gg}1$ emitters driving an optical resonator mode. We derive a general model that captures essential physics of such devices while not depending on specific microscopic details. We find the conditions under which the coherence times are exponentially long, thus surpassing the fundamental limitation on the coherence times of common lasers. For this we study the noise in the device. In particular, we are interested in the rate of large fluctuations of the light field in the limit where the typical fluctuations are small. The large fluctuations are responsible for switching of the laser between stable states of radiation and therefore determine the coherence time.
Recently, we have proposed the half-Josephson laser (HJL): a device that combines lasing with superconducting leads, providing a locking between the optical phase and the superconducting phase difference between the leads. In this work, we propose and investigate two setups derived from a superconducting quantum interference device (SQUID), where two conventional Josephson junctions are replaced by two HJLs. In the first setup, the HJLs share the same resonant mode, while in the second setup two separate resonant modes of the two lasers are coupled optically. We dub the setup ``light-superconducting interference device'' (LSID). In both setups, we find the operating regimes similar to those of a single HJL. Importantly, the steady lasing field is significantly affected by the magnetic flux penetrating the SQUID loop, with respect to both amplitude and phase. This provides opportunities to tune or even quench the lasing by varying a small magnetic field. For the second setup, we find a parameter range where the evolution equation for the laser fields supports periodic cycles. The fields are thus modulated with the frequency of the cycle resulting in an emission spectrum consisting of a set of discrete modes. From this spectrum, two modes dominate in the limit of strong optical coupling. Therefore, the LSID can be also used to generate such modulated light.
In this dissertation, we study a novel class of laser devices, referred to as half-Josephson lasers (HJL). Here, lasing at half the Josephson frequency is induced by a parametric instability, resulting from an oscillating supercurrent flowing through a Josephson junction that contains quantum emitters. The device combines the electronic coherence of superconductivity with the optical coherence of lasers, resulting in a phase lock between the optical phase and the superconducting phase difference across the junction. Apart from the introductory first chapter, this dissertation consists of two parts. In the first part, the essentials of HJL devices are investigated. First, we study a model containing a Josephson junction with a single quantum emitter. Spontaneous switchings in the quantum emitter lead to decoherence of the laser. After this, a general HJL model is derived for the case of many quantum emitters driving the laser mode. Here, small fluctuations in the laser lead to a broad background in the laser spectrum. Large fluctuations, occurring on exponentially long timescales, cause decoherence. In the second part of the dissertation, two possible applications of the HJL are investigated, both exploiting the phase lock. First, a well-known optical feedback technique is found to lead to significant stabilization of fluctuations in the bias voltage of the HJL, which cause drift of the optical and superconducting phases. After this, a HJL device is proposed based on the Superconducting Quantum Interference Device. In this `light-superconducting interference device’ (LSID), magnetic fields can be used to manipulate the laser light. The LSID is also shown to facilitate multimode lasing.
A recently proposed device, dubbed half-Josephson laser, provides a phase-lock between the optical phase and the superconducting phase difference between the leads of the device. In this paper we propose to utilize this phase-lock for stabilization of voltage fluctuations, by two optical feedback schemes. The first scheme involves a single half-Josephson laser and allows to significantly decrease the diffusion coefficient of the superconducting phase difference. The second scheme involves a stable optical source and a fluctuating half-Josephson laser and permits quenching of the diffusion of the relative phase of the lasers. This opens up perspectives of the optical control of the superconducting phase and voltage fluctuations.
We propose a new method of generating nonclassical optical field states. The method uses a semiconductor device, which consists of a single quantum dot as active medium embedded in a p- i- n junction and surrounded by a microcavity. Resonant tunneling of electrons and holes into the quantum dot ground states, together with the Pauli exclusion principle, produce regulated single photons or regulated pairs of photons. We propose that this device also has the unique potential to generate pairs of entangled photons at a well-defined repetition rate.
I report measurements of two different types of superconducting devices illuminated by 780 nm light, one of the wavelengths needed in a proposed atom-superconductor hybrid quantum system. I illuminated a thin-film Al lumped-element resonator and observed the resonator quality factor and resonance frequency as a function of illumination intensity, microwave power, and temperature. The resonator was mounted in a 3d aluminum cavity. The variation in optically-induced loss due to microwave power was similar to the behavior expected for loss from a distribution of two-level systems. Although this behavior may suggest the presence of optically activated two-level systems, I found that the loss is better explained by the presence of nonequilibrium quasiparticles generated by the illumination and excited by the microwave drive. I described a model of the system where optical absorption creates an effective source of phonons and solved the coupled quasiparticle-phonon rate equations. I found good agreement between the simulation and the measured resonator quality factor and frequency shift as a function of temperature, microwave power, and optical illumination. I fabricated a transmon qubit and studied the qubit transition frequency and relaxation time as a function of illumination intensity and temperature. The qubit was mounted in a 3d aluminum cavity and coupled to the cavity forming a Jaynes-Cummings system. Qubit relaxation showed non-exponential behavior that I fit to a quasiparticle fluctuation model with two characteristic times. The transition frequency and both characteristic times decreased with increasing illumination intensity. For comparison, I described a nonequilibrium quasiparticle model for the expected frequency shift and relaxation time due to quasiparticle tunneling through the Josephson junction. While the quasiparticle simulation predicted the general qualitative behavior of the frequency shift and relaxation time, there were some significant discrepancies with the data. This suggests the model needs to be extended, for example by including a different gap in the two superconductor layers forming the junction, and by taking into account other possible sources of loss and decoherence.