Howard Carmichael

In 1976, while Carmichael was still a graduate student, he and his doctoral supervisor Dan Walls published a seminal paper [15][16] that predicted photon antibunching, which led to the experimental demonstration of the quantum nature of light.[6][7] The paper was based on their work with master equation techniques to describe open quantum systems, which Carmichael began during his masters. They had decided to investigate resonance fluorescence because it seemed like a good application of their master equations to two coupled open quantum systems. There was considerable international interest among the fledgling quantum optics community, in both experimental and theoretical resonance fluorescence.[6] Using their newly developed master equation techniques, Walls and Carmichael derived the form of the fluorescence spectrum that agreed with previous experimental results.[17] They went on to calculate the second-order correlation function to explore the statistics of resonance fluorescence. They were able to use the correlation function to explain how jumps of an emitting atom imprint on the emitted photon stream. They predicted that the correlation function should drop to zero at zero time delay and suggested a Quantum Electrodynamics (QED) experiment to test their predictions. These experiments were performed shortly afterwards providing evidence of the quantum character of the light emitted in resonance fluorescence.[7][6]

Carmichael developed quantum trajectory theory (QTT) in the early 1990s,[11][12] around the same time as the separate formulations by Dalibard Castin & Mølmer, and by Zoller, Ritsch & Dum). QTT (also known as quantum jump method or Monte Carlo wave function (MCWF)) is a formulation of quantum mechanics that tracks the path that a quantum object takes through the space of all its possible states as it is measured.[10]

QTT is compatible with the standard formulation of quantum theory, as described by the Schrödinger equation, but offers a more detailed view.[3] The Schrödinger equation, is a probabilistic theory. It gives the probability of finding a quantum system in each of its possible states should a measurement be made. This is useful for predicting average measurements of large ensembles of quantum objects but it does not describe the behaviour of individual particles. QTT fills this gap by offering a way to describe the trajectories of individual quantum particles that obey the probabilities given by the Schrödinger equation.[3][18] QTT also works with open quantum systems that interact with their environment unlike the Schrödinger equation which only describes a quantum system in isolation.[10] QTT has become particularly popular since the technology has become available to efficiently control and monitor individual quantum systems as it can predict how individual quantum objects such as particles will behave when they are observed.[3]

In QTT open quantum systems are modelled as scattering processes, with classical external fields corresponding to the inputs and classical stochastic processes corresponding to the outputs (the fields after the measurement process).[1] The mapping from inputs to outputs is provided by a quantum stochastic process that is set up to account for a particular measurement strategy (eg., photon counting, homodyne/heterodyne detection, etc).[8]

QTT addresses the measurement problem in quantum mechanics by providing a detailed description of what happens during the so-called "collapse of the wave function". It reconciles the concept of a quantum jump with the smooth evolution described by the Schrödinger equation. The theory suggests that "quantum jumps" are not instantaneous but happen in a coherently driven system as a smooth transition through a series of superposition states.[18] This prediction was tested experimentally in 2019 by a team at Yale University led by Michel Devoret and Zlatko Minev in collaboration with Carmichael and others at Yale University and the University of Auckland. In their experiment they used a superconducting artificial atom to observe a quantum jump in detail, confirming that the transition is a continuous process that unfolds over time. They were also able to detect when a quantum jump was about to occur and intervene to reverse it, sending the system back to the state in which it started.[19] This experiment, inspired and guided by QTT, represents a new level of control over quantum systems and has potential applications in correcting errors in quantum computing in the future.[19][20][21][22][10][18][23]