We consider a single-mode optical cavity field with simultaneous dissipative and amplifying couplings to a reservoir via a two-state system. In previous works, the reservoir has either solely absorbed energy (detector setup) or added energy (amplifying setup) to the cavity. In this work, we allow both interactions simultaneously and derive a reduced dynamic model for the optical field. Our model includes four physical parameters: the field-two-state system coupling γ, the excitation and de-excitation couplings of the two-state system to the reservoir λA and λD, respectively, and the mirror losses of the cavity C. We show that, depending on the parameters, our setup can operate as a detector, a light-emitting diode or a laser. We also consider single-photon subtraction and addition schemes based on beam splitters and calculate the output fields and the probabilities of the subtraction and addition events. Furthermore, we discuss which are the parameter regimes in which our model is equivalent to beam splitter-based schemes.
We consider a single-mode optical cavity field with simultaneous dissipative and amplifying couplings to a reservoir via a two-state system. In previous works, the reservoir has either solely absorbed energy (detector setup) or added energy (amplifying setup) to the cavity. In this work, we allow both interactions simultaneously and derive a reduced dynamic model for the optical field. Our model includes four physical parameters: the field-two-state system coupling γ, the excitation and de-excitation couplings of the two-state system to the reservoir λA and λD, respectively, and the mirror losses of the cavity C. We show that, depending on the parameters, our setup can operate as a detector, a light-emitting diode or a laser. We also consider single-photon subtraction and addition schemes based on beam splitters and calculate the output fields and the probabilities of the subtraction and addition events. Furthermore, we discuss which are the parameter regimes in which our model is equivalent to beam splitter-based schemes.
We consider simultaneous dissipative and amplifying coupling of cavity fields to multiple two-state systems. We derive a master equation for optical field in a leaky cavity coupled to a reservoir through multiple two-state systems. In our previous works we have limited our study to systems where the reservoir either solely absorbs energy (detector setup) or adds energy (amplifying setup) to the cavity through a single two-state system. In this work we allow both interactions simultaneously and derive a reduced dynamic model for the optical field. We also generalize our model to cover the coupling of the field to several two state systems and discuss its connection to macroscopic interaction, e.g., in semiconductors. Our model includes four physical parameters: the field two-state system coupling $\ensuremath{\gamma}$, the excitation and deexcitation couplings of the two-state system by the reservoir ${\ensuremath{\lambda}}_{A}$ and ${\ensuremath{\lambda}}_{D}$, respectively, and the mirror losses of the cavity C. We solve the steady-state fields at different regimes of these physical parameters. Furthermore, we show that, depending on the parameters, our model can describe the operation of a detector, a light emitting diode, or a laser.
Analysis of quantum optical experiments and the simulation of optical devices require detailed quantum mechanical models, especially in the case of weak optical fields. In this thesis the quantum dynamics of cavity fields are investigated and new tools for modeling cavity fields interacting with an energy reservoir are developed. Using the quantum trajectory approach the field dynamics during photon detection processes are investigated. Two experimentally feasible detector models, the resolving and the non-resolving detector scheme, are derived and applied to single photon detection and coincidence photon detection experiments. Furthermore, equivalence of the cavity field model to the beam splitter based single photon subtraction and addition schemes is shown. In addition to the detection schemes described above, a reduced model for fields in a non-ideal cavity interacting with a dissipative and amplifying reservoir through multiple two state systems is derived. The reduced model can be used to describe e.g. light emitting diodes and lasers depending on the relative strengths of the losses and energy injection. In these cases the model reproduces fields that approach a thermal or a coherent field, respectively. The derived models can be applied to wide variety of cavity field experiments. The reduced field model can be applied to modeling the optical fields of semiconductor devices or to describe cavity field based quantum information processing experiments. Furthermore, fundamental quantum optics experiments of single photon addition, single photon subtraction, coincidence detection, and their combinations can be analyzed using the derived models.
We derive a generalized quantum jump superoperator that can be used in the quantum trajectory description of single photon detectors, light-emitting diodes (LEDs), and lasers. Our model describes an optical single-mode cavity field coupled to a reservoir through a two-state quantum system and includes three physical parameters: the coupling of the field to the two-state system, the coupling of the two-state system to the reservoir, and the cavity loss rate. In this setup, the two-state system can act as a photodetector or as an energy-adding mechanism. In the first case, we assume that the reservoir acts as a damping mechanism for an ideal cavity and derive reduced field operators describing the photon detection events. Our model coincides with the commonly known quantum trajectory based photon counting models at the weak- and strong-coupling limits and is, furthermore, also applicable between their validity regimes. In the second case, we assume that the reservoir injects energy into a lossy cavity through the two-state system. Again we derive the reduced field operators describing photon creation events into the lossy cavity. We show that this setup can act as an LED or as a laser depending on the strength of the injection. We also investigate how the setup operates at the close proximity of the lasing threshold.
In atomic-scale or quantum physics, an electromagnetic field is composed of photons, optical packets so small that a typical laser pointer with 1mW of power emits billions of them each second. Being able to take away or add a single photon in a light field at will would be useful for accurate engineering of quantum states. Such pure single photons are ideal for carrying and manipulating information in emerging quantum technologies, but generating them still is very challenging. In quantum physics, subtraction or addition of a photon is not a deterministic process. Instead, the probability is proportional to the number of photons originally in the electromagnetic field. This is described by the equation â|n〉 = √ n|n − 1〉 and â†|n〉 = √ n+ 1|n + 1〉, where â and ↠are annihilation and creation operators, respectively, representing the action of subtracting and adding a photon in a field composed of n photons.1 Such single-photon operations were limited to pure theoretical discussions until 2004, when Grangier and coworkers found a simple way to subtract a photon2 from a field. Passing through a beam splitter of high transmittivity, some photons can be split from the initial field. A ‘click’ detected in the photodetector in the reflected channel means one photon has been subtracted from the field: see Figure 1(a). When the initial field is composed of a small number of photons, the effect is dramatic and may even completely change the characteristics of the field. For example, let us take an initial single-mode squeezed state generated by ‘degenerate’ parametric down-conversion, which is an optical nonlinear process that converts a pump photon into two twin photons with half the pump photon energy. (This state is well known for its quantum noise squeezed into one quadrature at the expense of expanded noise in the other quadrature.) In order to visualize the noise properties and characteristics of the squeezed state, a probability-like function, such Figure 1. Setups to subtract (a) and add (b) a single photon from/to a light field. ρin and ρout denote the density operators of the input and output fields; BS is a low-reflectivity beam splitter; PDC is a nonlinear crystal where parametric down-conversion takes place; â and ↠denote on/off photodetectors.
We derive the quantum mechanical description of light-matter interactions in optical cavities characterized solely by radiative decay. Unique to radiative decay is the conservation of photon number and coherence, in stark contrast to absorptive losses. This prohibits the description of such cavities by traditional means, e.g., coupling it to a bath of harmonic oscillators into which energy is dissipated. Here, we propose a description of cavities with radiative decay by introducing cavity and noise operators in terms of scattering modes. A multimode input-output formalism to predict measurable far field quantities arises naturally. We apply our general model to the special case of the single excitation regime. We find dynamics reminiscent of the dissipative Jaynes-Cummings model, but with vanishing backaction and a rich temporal and spectral structure of the output modes.
Within the framework of a two-dimensional microscopic, purely quantum mechanical model, we analyse the dynamics of single-photon wave packets interacting with optical elements (beam splitters, mirrors), modelled as systems of two-level atoms. That is, we utilize a two-dimensional cavity to simulate the quantum behaviour of simple optical components and networks made thereof. The field is quantized using the canonical procedure, and only the basis states with one unit of excitation are included. This, however, covers linear optical phenomena. The field is taken to interact with localized atoms through a dipole interaction. Using different configurations of atoms, and choosing their frequencies to be resonant or off-resonance, we can model mirrors, beam splitters, focusing devices and multicomponent systems. Thus we can model arbitrary linear networks of optical components. We show the time evolution of a photon wave packet in an interferometer as an example. As the state of the field is known at each instant, spectral properties and spatial coherence can immediately be obtained from the simulations. We also know the states of the two-level atoms constituting the components, which allows us to consider their quantum behaviour. Here the decay of an excited atom into the vacuum state of the electromagnetic field in the two-dimensional cavity is studied.