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Physical Review Letters

Bright Sub-Poissonian Light through Intrinsic Feedback and External Control

Victor Canela, H. J. Carmichael

Published Feb 14, 2020• 9 citations
Publisher

Abstract

Balancing nonlinear gain and loss automatically generates sub-Poissonian light, through negative feedback, when the gain is significantly reduced (increased) by the addition (subtraction) of a single photon. We show that micromaser trapping states can provide the necessary feedback in the presence of photon loss and, with the addition of external parametric control, realize a photon number on the order of 100 and a Mandel Q parameter of -0.998, i.e., number squeezing of 27 dB.

DOI
10.1103/physrevlett.124.063604

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Balancing nonlinear gain and loss automatically generates sub-Poissonian light, through negative feedback, when the gain is significantly reduced (increased) by the addition (subtraction) of a single photon. We show that micromaser trapping states can provide the necessary feedback in the presence of photon loss and, with the addition of external parametric control, realize a photon number on the order of 100 and a Mandel Q parameter of -0.998, i.e., number squeezing of 27 dB.
Nonclassical states of light, such as number-squeezed light, with fluctuations below the classical shot noise level, have important uses in metrology, communication, quantum information processing, and quantum simulation. However, generating these nonclassical states of light, especially with high intensity and a high degree of squeezing, is challenging. To address this problem, we introduce a new concept which uses gain to generate intense sub-Poissonian light at optical frequencies. It exploits a strongly nonlinear gain for photons which arises from a combination of frequency-dependent gain and Kerr nonlinearity. In this laser architecture, the interaction between the gain medium and Kerr nonlinearity suppresses the spontaneous emission at high photon number states, leading to a strong "negative feedback" that suppresses photon-number fluctuations. We discuss realistic implementations of this concept based on the use of solid-state gain media in laser cavities with Kerr nonlinear materials, showing how 90% squeezing of photon number fluctuations below the shot noise level can be realized.
We propose a feedback scheme to control the photon statistics in a micromaser/laser cavity, using the system output as the control signal, which generates a highly nonclassical field whose Mandel-Q parameter is even lower than −0.9 and mean photon number much greater than unity. We demonstrate that the so-obtained system constitutes a continuous-wave (CW) quasi-Fock state source, the emission of which exhibits a sub-Poissonian photocount distribution as well as the photon anti-bunching property.
In this thesis, we study a system consisting of qubits—two-level quantum systems— interacting in the strong-coupling regime for a finite amount of time with a mode of the electromagnetic field inside a resonator. In particular, we are interested in the dynamics of the photon number and the possibility of controlling its statistics to produce sub-Poissonian light. To describe the system we use quantum trajectory theory where the time evolution of the state vector consists of both a continuous part and jumps, which account for the resonator losses. We also incorporate a variable number of qubits (changing in time) interacting with the mode. A computer simulation was developed and optimised to calculate the quantum trajectories. When one sets the qubits initially to the excited state and fixes the interaction time accordingly, so-called “trapping states” (photon numbers which block the addition of a photon by a single qubit) appear. These states are instrumental in the generation of sub-Poisson fields, for some cases even when the number of interacting qubits follow a Poisson process. We take advantage of the existence of trapping states to implement control protocols based on the measurement of the output field of the resonator, with the objective of lowering the uncertainty in the number of photons. Furthermore, we explore the possibility of creating a source of sub-Poissonian pulses by first using a random interaction time (which bypasses the trapping states) and then utilising the control protocols developed. We are able to achieve fields with a Mandel Q parameter of QM = −0.98 and a photon number of n 68.
We present a quantum theory of the micromaser which allows for arbitrary (sub- as well as super-Poissonian) fluctuations of the pumping beam. It handles the interaction with the active atoms (gain) and cavity decay (loss) on an equal footing. In conventional reservoir theory the rate of change of the cavity field is a sum of the changes due to separate interactions with the individual reservoirs, i.e., the interactions are uncorrelated. In our approach, corrections to reservoir theory arise. They contain the commutator of the gain and loss operators. The magnitude of these additional terms is characterized by the quantity p/Nex{\mathit{N}}_{\mathrm{ex}}Nex​ where p is a parameter describing pump-beam fluctuations. The parameter is, in fact, the negative of the Mandel Q parameter of the pump beam so that p=1 corresponds to regular pumping, p=0 to Poissonian one and p0 to super-Poissonian pump beam fluctuations. Nex{\mathit{N}}_{\mathrm{ex}}Nex​ is the number of excited atoms passing through the cavity during the lifetime of the intracavity field. Thus we recover the conventional reservoir limit if p=0 and/or Nex{\mathit{N}}_{\mathrm{ex}}Nex​ is large. In all other cases the interactions with the gain and loss reservoirs are correlated. We exploit some of the consequences of the additional terms, presenting analytical as well as numerical results for the steady-state photon statistics (mean photon number and photon-number fluctuations, in particular) without resorting to the p expansion.