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.
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 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.
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.
Quantum opto-mechanics is a fast moving, broad research field which aims to investigate and control the interaction of light and the quantized motion of mechanical objects and the coupling between them. This allows one to engineer the mechanical quantum state by controlling and measuring the electromagnetic field, and conversely, to control the dynamical evolution of the optical field via its interaction with a mechanical system. Mechanical resonators are accessible in many different shapes and sizes, from kilogram scales in experiments that test gravitational theories to micro- and nano-scales in resolved sideband regime, where the frequency of the mechanical resonator is larger than the bandwidth of the optical cavity. In this regime, it is possible to cool the mechanical object to the ground state which allows a high degree of control and the ability to prepare interesting non-classical states, states that could aid in investigating the quantum dynamics of macroscopic objects. The field of quantum opto-mechanics is a promising testbed for quantum control technologies, such as fundamental tests of quantum mechanics, ultra-sensitive quantum sensors for precise measurements, phonon lasing, mechanical memories with long lifetime and quantum information processing. Furthermore, experiments are progressing toward strong opto-mechanical coupling regimes with single photons. This creates a platform that can take advantage of the nonlinear optical interactions to generate highly non-classical states in such light-matter interfaces. Photonic systems working in the single photon regime will be promising for low power applications and also for implementations of quantum information and computation. Motivated by these applications, this thesis consists of theoretical studies in the context of single photonics. This includes investigating non-classical mechanical state generation and mechanically controlling the dynamical evolution of optical fields in the strong coupling regime single photon opto-mechanics and furthermore, proposing a quantum sensor using single photonics. In this regard, we employ three important formalisms to treat and measure open quantum systems with non-Gaussian input fields: the conditional and unconditional cascaded master equations, Fock-state master equations and input-output Langevin equations. In the context of opto-mechanics, the system to be investigated is composed of two optical cavities with a coupling modulated via a mechanical resonator. In one case, a sequence of single photons are irreversibly sent to one of the optical cavities. After photons go through the opto-mechanical interaction, photon counting measurements are performed on the cavity output, conditionally steering the mechanical state to a highly non-classical Fock state. Numerical calculations are performed to predict the experimental parameters needed to generate a mechanical Fock state before the mechanical object is thermalized. In another case, the same opto-mechanical scheme is employed to conversely modify the state of the optical mode by engineering the state of the mechanical degree of freedom. In this case, it is shown that the opto-mechanical system operates as an effective beam splitter for the input single photons, with a transmission that can be controlled by tuning the number of excitations in the bulk mechanical resonator. When the mechanical resonator has a small coherent amplitude it acts as a quantum control, entangling the optical and mechanical degrees of freedom. As the coherent amplitude of the resonator increases, it acts as a classical control for the input photons. Finally, we propose a novel multi-purpose sensor architecture that can be used for force, refractive index and possibly local temperature detection. In this scheme, two coupled cavities behave as an effective beam splitter. This sensor is based on fourth order interference (the Hong-Ou-Mandel effect) and requires a sequence of single photon pulses and consequently has low pulse power. Changes in the parameter to be measured induce variations in the effective beam splitter reflectivity and result in changes to the visibility of interference. We propose that this generic scheme could be implemented with coupled L3 photonic crystal cavities and find that this system, which only relies on photon coincidence detection and does not need any spectral resolution, can estimate forces as small as 10-7 Newtons and can measure one part per million change in refractive index using a very low input power of 10-10 W.
Time development of electromagnetic fields in closed cavities under continuous detection of photons continues to be a subject of confusing controversy. Recently Dodonov et al. [Phys. Rev. A, 75, 013806, 2007] argued that their model of quantum superoperators (E model) invalidates some of the predictions of the previously introduced photon counting model of Srinivas and Davies [J. Mod. Optic. 28, 981, 1981] (SD model). Both the SD and the E models are based on two postulated quantum jump superoperators: (1) the one-count operator corresponding to the absorption of a single photon and (2) the no-count operator. In this work we develop a stochastic difference equation that describes the dissipative coupling of the cavity field and the detector. The difference equation is based on non-perturbative treatment of the cavity-detector coupling. In spite of being non-integrable due to the coupling of the detector with an external reservoir it can be used to derive the exact forms of the quantum jump superoperators. When applied to a particular photon counting measurement our theory gives predictions identical with those of the SD model which should be considered a non-perturbative and ab-initio result. It is pointed out that available experimental results coincide with the results given by the ab-initio SD model. We summarize some of the key characteristics of cavity fields and photon counting processes to demonstrate that the results given by the SD model are consistent with the principles of quantum mechanics while those given by the E model are not.
Recently Parigi et al. ( Science , 317 (2007) 1890 ) measured the statistics of a photon-subtracted and a photon-added thermal field. They showed that the measurements agree with the theoretical predictions of the beam splitter (BS) model. We show the equivalence of the quantum trajectory approach and the BS model in photon subtraction by deriving the BS model from the generalized photon counting operators. Our photon counting operators, corresponding to measurements using a resolving detector and a nonresolving detector, are generalization of the standard quantum jump approach. Our model is exact from weak quantum fields to the classical limit of strong fields. We show that our generalized photon counting operators reproduce exactly the results of the BS model when the reflection probability of the beam splitter is equated with the absorption probability of a photon in the standard quantum jump model of cavity field damping. Our theory can explain the recent experimental results of Parigi et al. and shows how similar experiments can be made to test the photon subtraction for the whole range of electromagnetic field intensities ranging from quantum to classical limit. We propose new experiments to test the generalized photon counting operators in the intermediate regime between the quantum and classical limits.