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arXiv:1211.6877 · Physical Review B

Lasing at half the Josephson frequency with exponentially long coherence times

Frans Godschalk, Yuli V. Nazarov

Published Mar 18, 2013• 9 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevb.87.094511

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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≫1N\ensuremath{\gg}1N\ensuremath≫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.
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.
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.
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.
Superconducting electronic devices have reemerged as contenders for both classical and quantum computing due to their fast operation speeds, low dissipation, and long coherence times. An ultimate demonstration of coherence is lasing. We use one of the fundamental aspects of superconductivity, the ac Josephson effect, to demonstrate a laser made from a Josephson junction strongly coupled to a multimode superconducting cavity. A dc voltage bias applied across the junction provides a source of microwave photons, and the circuit's nonlinearity allows for efficient down-conversion of higher-order Josephson frequencies to the cavity's fundamental mode. The simple fabrication and operation allows for easy integration with a range of quantum devices, allowing for efficient on-chip generation of coherent microwave photons at low temperatures.
By irradiating with a single ultrafast laser pulse a superconducting electrode of a Josephson junction, it is possible to drive the quasiparticles (qp's) distribution strongly out of equilibrium. The behavior of the Josephson device can, thus, be modified on a fast time scale, shorter than the qp's relaxation time. This could be very useful, in that it allows fast control of Josephson charge qubits and, in general, of all Josephson devices. If the energy released to the top layer contact S1S1S1 of the junction is of the order of $\ensuremath{\sim}\ensuremath{\mu}J$, the coherence is not degradated because the perturbation is very fast. Within the framework of the quasiclassical Keldysh Green's function theory, we find that the order parameter of S1S1S1 decreases. We study the perturbed dynamics of the junction, when the current bias is close to the critical current, by integrating numerically its classical equation of motion. The optical ultrafast pulse can produce switchings of the junction from the Josephson state to the voltage state. The switches can be controlled by tuning the laser light intensity, the pulse duration, and the bias current of the Josephson junction.