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A New Quantum Limit on Laser Linewidth

Chenxu Liu, Maria Mucci, Xi Cao, Meenakshi Dutt, Michael Hatridge, David Pekker

Published Sep 7, 2020• 2 citations
OpenAlex

Abstract

Due to their high coherence, Lasers are a ubiquitous tool in science. The standard quantum limit for the phase coherence time was first introduced by [A. Schawlow and C. Townes, Phys. Rev. 112, 1940 (1958)], who showed that the minimum possible laser linewidth is determined by the linewidth of the laser cavity divided by twice the number of photons in the cavity. Later, Wiseman showed theoretically that by using Susskind-Glogower (SG) operators to couple the gain medium to the laser cavity it is possible to eliminate pump noise, but not loss noise. This decreases the minimum laser linewidth, though only by a factor of two. In this article, we show that by engineering the coupling between the laser cavity and the output port it is possible to eliminate most of the loss noise as well and construct a laser that has a vastly narrower linewidth, narrower than the standard quantum limit by a factor equal to the number of photons in the laser cavity. We establish a roadmap for building such a device in the laboratory by using Josephson junctions and linear circuit elements to build coupling circuits that behave like SG operators for a range of cavity photon occupancies and using them to couple the laser cavity to both the gain medium and the output port. This device could be an ultra-coherent, cryogenic light source for microwave quantum information experiments. Further, our laser provides highly squeezed light and could be modified to provide designer quantum light which is an important resource for CV/linear optical quantum computing, readout of quantum states in superconducting quantum computers, quantum metrology, and quantum communication. Finally, our proposal relies on the tools and elements of superconducting quantum information, and thus is a clear example of how quantum engineering techniques can inspire us to re-imagine the limits of conventional quantum systems such as the laser.

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Due to its high coherence in transmission over a large distance in the ambient environment, the quantum optical system has been a prevailing platform for long-distance quantum communication, which was recently realized over a continental distance with a low earth orbit satellite and ground stations [102, 70]. However, the pure quantum optical system has so far shown weak interactions between photon and matter, which makes it inefficient in carrying out deterministic quantum gates for quantum repeater based scalable quantum network and quantum computing. On the other hand, superconducting quantum systems operating in the microwave domain with Josephson junction transmon qubits have proven to be capable of efficient deterministic quantum operations on quantum states [86, 87, 66]. Nevertheless, such architecture is prone to errors and decoherence due to cross-talk between microwave elements in a large-scale superconducting quantum circuit. Furthermore, superconducting systems, in general, also have large footprint (100s um) elements (resonators and superconducting quantum bits) [92, 60] that limit the ability to scale up a superconducting quantum system. Moreover, microwave quantum circuits require cooling to around 10 mK, making it unsuitable for communicating quantum information outside a dilution refrigerator (DF). Micro- and nano- acoustic elements have been extensively used in conventional integrated information processing systems due to their compactness and high coherence [97]. Acoustic systems in quantum engineering also have the advantage of being a platform for universal couplings between various quantum systems including spins, optical photons, and superconducting circuits. As it will be discussed in this thesis, elements critical to scalable optical quantum network and superconducting quantum circuit can be constructed relying on the cavity optomechanics and piezoelectric interactions. Optomechanical interaction is concerned with the light pressure coupling of cavity mechanical deformation to a strong optical field. This interaction has allowed the close to mechanical ground state cooling of mechanical resonators using laser and the ultra-sensitive displacement measurement that led to the detection of gravitational waves in the LIGO collaboration [125, 25]. Optomechanical crystals (OMCs) are lithographically patterned devices which contain a periodic structure that host bandgaps for both optical band electromagnetic waves and microwave band acoustic waves. A properly engineered defect in the crystal can confine and localize acoustic and electromagnetic modes of similar wavelengths into a small mode volume [17, 20, 21]. A strong optomechanical coupling, which can be achieved between such strongly confined co-localized optical and acoustic modes, can be used in engineering the quantum state of mechanical motion to realize useful quantum devices such as a high-coherence quantum memory [74] and an optomechanical high efficiency optical isolator for unidirectionally connecting distant optical cavities via an acoustic bus [37]. To strongly couple the mechanical degree of freedom with a superconducting quantum circuit, various methods can be used, ranging from electromechanic coupling (electric coupling to a mechanically compliant capacitor), magnetomechanical coupling (magnetic coupling to a vibrating SQUID loop), and piezoelectric coupling. The recent advent of quantum acoustics [23, 8, 9] was realized with the strong piezoelectric coupling between a superconducting transmon qubit and a high-coherence mechanical resonator. The engineered strong piezoacoustic coupling provides the possibility to carry out deterministic ultra-high fidelity two-qubit quantum gates on non-classical mechanical quantum states [52]. This ability together with the recent demonstration of ultra-long phonon lifetime mechanical resonators show the possibility of integrating the ultra-high quality mechanical resonator as a compact quantum memory element and even a new ultra-compact (10s um) quantum bit architecture for scalable superconducting quantum circuits. Furthermore, the strong piezoelectric coupling that can transduce quantum state in a superconducting circuit into mechanical wave also makes it possible to efficiently transduce a quantum state between a superconducting quantum circuit and a telecommunication band optical channel via a mechanical waveguide connected to an optomechanical crystal cavity.

•Sep 9, 2019•0 citations
Due to their high coherence, Lasers are a ubiquitous tool in science. The standard quantum limit for the phase coherence time was first introduced by [A. Schawlow and C. Townes, Phys. Rev. 112, 1940 (1958)], who showed that the minimum possible laser linewidth is determined by the linewidth of the laser cavity divided by twice the number of photons in the cavity. Later, Wiseman showed theoretically that by using Susskind-Glogower (SG) operators to couple the gain medium to the laser cavity it is possible to eliminate pump noise, but not loss noise. This decreases the minimum laser linewidth, though only by a factor of two. In this article, we show that by engineering the coupling between the laser cavity and the output port it is possible to eliminate most of the loss noise as well and construct a laser that has a vastly narrower linewidth, narrower than the standard quantum limit by a factor equal to the number of photons in the laser cavity. We establish a roadmap for building such a device in the laboratory by using Josephson junctions and linear circuit elements to build coupling circuits that behave like SG operators for a range of cavity photon occupancies and using them to couple the laser cavity to both the gain medium and the output port. This device could be an ultra-coherent, cryogenic light source for microwave quantum information experiments. Further, our laser provides highly squeezed light and could be modified to provide designer quantum light which is an important resource for CV/linear optical quantum computing, readout of quantum states in superconducting quantum computers, quantum metrology, and quantum communication. Finally, our proposal relies on the tools and elements of superconducting quantum information, and thus is a clear example of how quantum engineering techniques can inspire us to re-imagine the limits of conventional quantum systems such as the laser.
Due to their high coherence, lasers are ubiquitous tools in science. We show that by engineering the coupling between the gain medium and the laser cavity as well as the laser cavity and the output port, it is possible to eliminate most of the noise due to photons entering as well as leaving the laser cavity. Hence, it is possible to reduce the laser linewidth by a factor equal to the number of photons in the laser cavity below the standard quantum limit. We design and theoretically analyze a superconducting circuit that uses Josephson junctions, capacitors and inductors to implement a microwave laser, including the low-noise couplers that allow the design to surpass the standard quantum limit. Our proposal relies on the elements of superconducting quantum information, and thus is an example of how quantum engineering techniques can inspire us to re-imagine the limits of conventional quantum systems.
The standard quantum limit to the linewidth of a laser for which the gain medium can be adiabatically eliminated is ${l}_{0}=\ensuremath{\kappa}/2\mathrm{n\ifmmode \bar{}\else \={}\fi{}}.$ Here $\ensuremath{\kappa}$ is the intensity damping rate and $\mathrm{n\ifmmode \bar{}\else \={}\fi{}}$ the mean photon number. This contains equal contributions from the loss and gain processes, so that simple arguments which attribute the linewidth wholly to phase noise from spontaneous gain are wrong. I show that an unstimulated gain process actually introduces no phase noise, so that the ultimate quantum limit to the linewidth comes from the loss alone and is equal to ${l}_{\mathrm{ult}}=\ensuremath{\kappa}/4\mathrm{n\ifmmode \bar{}\else \={}\fi{}}.$ I investigate a number of physical gain mechanisms which attempt to achieve gain without phase noise: a linear atom-field coupling with a finite interaction time, a nonlinear atom-field coupling, and adiabatic photon transfer using a counterintuitive pulse sequence. The first at best reaches the standard limit l0,{l}_{0},l0​, the second reaches 34l0,\frac{3}{4}{l}_{0},43​l0​, and the third reaches the ultimate limit of lult=12l0.{l}_{\mathrm{ult}}=\frac{1}{2}{l}_{0}.lult​=21​l0​.
The standard quantum limit to the linewidth of a laser for which the gain medium can be adiabatically eliminated is ℓ0=κ/2nˉ\ell_{0}=κ/2\bar{n}ℓ0​=κ/2nˉ. Here κκκ is the intensity damping rate and nˉ\bar{n}nˉ the mean photon number. This contains equal contributions from the loss and gain processes, so that simple arguments which attribute the linewidth wholly to phase noise from spontaneous gain are wrong. I show that an {\em unstimulated} gain process actually introduces no phase noise, so that the ultimate quantum limit to the laser linewidth comes from the loss alone and is equal to ℓult=κ/4nˉ\ell_{ult}= κ/4\bar{n}ℓult​=κ/4nˉ. I investigate a number of physical gain mechanisms which attempt to achieve gain without phase noise: a linear atom-field coupling with finite interaction time; a nonlinear atom-field coupling; and adiabatic photon transfer using a counterintuitive pulse sequence. The first at best reaches the standard limit ℓ0\ell_{0}ℓ0​, the second reaches 3/4ℓ03/4 \ell_{0}3/4ℓ0​, while the third reaches the ultimate limit of ℓult=1/2ℓ0\ell_{ult} = 1/2 \ell_{0}ℓult​=1/2ℓ0​.
The generation of very narrow linewidth light sources is of great importance in modern science. One such source is the superradiant laser, which relies on collectively interacting ultra long lived dipoles driven by incoherent light. Here we discuss a different way of generating spectrally pure light by coherently driving such dipoles inside an optical QED cavity. The light exiting cavity carries information about the detuning between the driving light and the atomic transition, but is also affected by the noise originating from all the decoherence processes that act on the combined atom-cavity system. We calculate these effects to obtain fundamental limits for frequency estimation and stabilization across a range of values of input light intensities and atom-light interaction strengths, estimate these limits in state-of-the-art cavity experiments with alkaline-earth atoms and identify favorable operating conditions. We find that the achievable linewidths are comparable to those of the superradiant laser.
We study a class of feedback oscillators realized by a phase-insensitive amplifier in positive feedback, where either the amplifier or the feedback element may determine the oscillator's linewidth. The spectral purity of the output of such a device originates from basic demands of quantum mechanics and causality. The resulting expression generalizes the Schawlow-Townes limit, which is itself one component of a standard quantum limit for feedback oscillators. Recently realized bad-cavity oscillators, such as superradiant lasers and solid-state masers, can saturate this generalized Schawlow-Townes limit. This limit can be surpassed through appropriate quantum engineering, for example, by atomic spin squeezing in a superradiant laser.
Due to its high coherence in transmission over a large distance in the ambient environment, the quantum optical system has been a prevailing platform for long-distance quantum communication, which was recently realized over a continental distance with a low earth orbit satellite and ground stations [102, 70]. However, the pure quantum optical system has so far shown weak interactions between photon and matter, which makes it inefficient in carrying out deterministic quantum gates for quantum repeater based scalable quantum network and quantum computing. On the other hand, superconducting quantum systems operating in the microwave domain with Josephson junction transmon qubits have proven to be capable of efficient deterministic quantum operations on quantum states [86, 87, 66]. Nevertheless, such architecture is prone to errors and decoherence due to cross-talk between microwave elements in a large-scale superconducting quantum circuit. Furthermore, superconducting systems, in general, also have large footprint (100s um) elements (resonators and superconducting quantum bits) [92, 60] that limit the ability to scale up a superconducting quantum system. Moreover, microwave quantum circuits require cooling to around 10 mK, making it unsuitable for communicating quantum information outside a dilution refrigerator (DF). Micro- and nano- acoustic elements have been extensively used in conventional integrated information processing systems due to their compactness and high coherence [97]. Acoustic systems in quantum engineering also have the advantage of being a platform for universal couplings between various quantum systems including spins, optical photons, and superconducting circuits. As it will be discussed in this thesis, elements critical to scalable optical quantum network and superconducting quantum circuit can be constructed relying on the cavity optomechanics and piezoelectric interactions. Optomechanical interaction is concerned with the light pressure coupling of cavity mechanical deformation to a strong optical field. This interaction has allowed the close to mechanical ground state cooling of mechanical resonators using laser and the ultra-sensitive displacement measurement that led to the detection of gravitational waves in the LIGO collaboration [125, 25]. Optomechanical crystals (OMCs) are lithographically patterned devices which contain a periodic structure that host bandgaps for both optical band electromagnetic waves and microwave band acoustic waves. A properly engineered defect in the crystal can confine and localize acoustic and electromagnetic modes of similar wavelengths into a small mode volume [17, 20, 21]. A strong optomechanical coupling, which can be achieved between such strongly confined co-localized optical and acoustic modes, can be used in engineering the quantum state of mechanical motion to realize useful quantum devices such as a high-coherence quantum memory [74] and an optomechanical high efficiency optical isolator for unidirectionally connecting distant optical cavities via an acoustic bus [37]. To strongly couple the mechanical degree of freedom with a superconducting quantum circuit, various methods can be used, ranging from electromechanic coupling (electric coupling to a mechanically compliant capacitor), magnetomechanical coupling (magnetic coupling to a vibrating SQUID loop), and piezoelectric coupling. The recent advent of quantum acoustics [23, 8, 9] was realized with the strong piezoelectric coupling between a superconducting transmon qubit and a high-coherence mechanical resonator. The engineered strong piezoacoustic coupling provides the possibility to carry out deterministic ultra-high fidelity two-qubit quantum gates on non-classical mechanical quantum states [52]. This ability together with the recent demonstration of ultra-long phonon lifetime mechanical resonators show the possibility of integrating the ultra-high quality mechanical resonator as a compact quantum memory element and even a new ultra-compact (10s um) quantum bit architecture for scalable superconducting quantum circuits. Furthermore, the strong piezoelectric coupling that can transduce quantum state in a superconducting circuit into mechanical wave also makes it possible to efficiently transduce a quantum state between a superconducting quantum circuit and a telecommunication band optical channel via a mechanical waveguide connected to an optomechanical crystal cavity.