Double-diffraction Raman interference is a novel interference scheme developed in recent years. It has a potentially high measurement precision due to the symmetric interference loop with identical internal states. In this paper, we analyze the high-order diffraction process in double-diffraction Raman interference and derive state evolution equations that include multiple diffraction processes. The population evolution of the states and the Mach-Zehnder interference fringe are calculated under the action of a Raman laser. The thermal momentum distribution averaging and state grouping methods are employed to solve the problem of decoherence at different interference exit ports. We compare the phase shifts calculated by integrating the sensitivity function and the two-photon frequency shift and by numerically solving the state evolution equations with high-order diffraction states. The good agreement between the results of the two methods shows that the two-photon frequency shift is the main reason for the phase shift induced by the higher-order diffraction states. Finally, the test error of an equivalent principle test experiment due to this effect is analyzed. This paper may be helpful for the analysis and suppression of the systemic error in such experiments.
Double-diffraction Raman interference is a novel interference scheme developed in recent years. It has a potentially high measurement precision due to the symmetric interference loop with identical internal states. In this paper, we analyze the high-order diffraction process in double-diffraction Raman interference and derive state evolution equations that include multiple diffraction processes. The population evolution of the states and the Mach-Zehnder interference fringe are calculated under the action of a Raman laser. The thermal momentum distribution averaging and state grouping methods are employed to solve the problem of decoherence at different interference exit ports. We compare the phase shifts calculated by integrating the sensitivity function and the two-photon frequency shift and by numerically solving the state evolution equations with high-order diffraction states. The good agreement between the results of the two methods shows that the two-photon frequency shift is the main reason for the phase shift induced by the higher-order diffraction states. Finally, the test error of an equivalent principle test experiment due to this effect is analyzed. This paper may be helpful for the analysis and suppression of the systemic error in such experiments.
Imperfect Raman pulses can lead to the formation of multiple interfering paths and affect the output of an atom interferometer in high-precision measurement.We study the effect of the imperfect Raman pulses on the interferometric fringe contrast and the phase shift in the three-pulse atom interferometer by using the evolution operator method.Analytical expressions expanded to the second-order fluctuation of imperfect pulses are derived, in which the effect of coupling the imperfect pulses with laser detuning and pulse duration is also considered.The result indicates that the second-order fluctuation of imperfect pulses is dominant, however, it can be nearly ignored in the current requirements of atomic experiments.Even so, theoretical analysis is very necessary as it may be helpful in proposing some schemes to improve the interference efficiency for future high-precision measurements with atomic interferometry.
In a retroreflective scheme with an atom initially at rest, atomic Raman diffraction adopts some of the properties of Bragg diffraction due to additional couplings to off-resonant momenta. As a consequence, double Raman diffraction has to be performed in a Bragg-type regime, where the pulse duration is sufficiently long to suppress diffraction into spurious orders. Taking advantage of this regime, double Raman allows for resonant higher-order diffraction. We study theoretically the case of third-order diffraction and compare it to first order as well as a sequence of first-order Raman pulses giving rise to the same momentum transfer as the third-order pulse. Moreover, we demonstrate that interferometry is possible, and we investigate amplitude and contrast of a third-order double Raman Mach-Zehnder interferometer. In fact, third-order diffraction constitutes a competitive tool for the diffraction of ultracold atoms and interferometry based on large momentum transfer since it allows one to reduce the complexity of the experiment as well as the total duration of the diffraction process compared to a sequence, at the cost of higher pulse intensities.
The use of retroreflection in light-pulse atom interferometry under microgravity conditions naturally leads to a double-diffraction scheme. The two pairs of counterpropagating beams induce simultaneously transitions with opposite momentum transfer that, when acting on atoms initially at rest, give rise to symmetric interferometer configurations where the total momentum transfer is automatically doubled and where a number of noise sources and systematic effects cancel out. Here we extend earlier implementations for Raman transitions to the case of Bragg diffraction. In contrast with the single-diffraction case, the existence of additional off-resonant transitions between resonantly connected states precludes the use of the adiabatic elimination technique. Nevertheless, we have been able to obtain analytic results even beyond the deep Bragg regime by employing the so-called ``method of averaging,'' which can be applied to more general situations of this kind. Our results have been validated by comparison to numerical solutions of the basic equations describing the double-diffraction process.
Using the electro-optical modulation method to generate Raman beams for cold atom interference is one of the better methods for constructing a more compact and robust laser system. But this way will generate some residual sidebands resulting in the additional interference phase shift, which can affect the measurement accuracy of cold atom interferometer. In order to weaken the effect of laser modulation sidebands on the phase shift of cold atom interference, a double-sideband suppressed-carrier modulation laser system for cold atom interference is constructed. Based on the designed laser system, the principle of double-sideband generation and suppression is analyzed in detail, and some residual sidebands are adjusted and controlled. Moreover, some important optical parameters that affect the phase shift of cold atomic interference, such as the initial distance between the Raman retro-reflection mirror and the atomic cloud, the interrogation time between two adjacent Raman pulses, the laser modulation depth and the initial velocity of the atomic cloud, are discussed and optimized. By optimizing these relevant parameters, the influence of residual modulation sidebands on the phase shift of cold atomic interference is weakened drastically. The research results indicate, making use of the method of double-sideband suppression, the phase shift of cold atomic interference can be optimized to 0.7 mrad when the initial distance between the Raman retro-reflection mirror and the atomic cloud is 105 mm, and the interrogation time between two adjacent Raman pulses is 82 ms. More importantly, this work can provide a method for weakening the influence of Raman sideband effect on the phase shift of cold atom interferometer, and the corresponding laser system can be applied to other inertial sensors such as atomic gravimeter or atomic gravity gradiometer.
This cumulative thesis consists of four publications [1-4], presented as three contributions (I) - (III), where the second one (II) consists of the joint publications [2,3]. All publications were written during the author's research activities at the Institute of Quantum Physics under the supervision of Prof. Dr. W. P. Schleich. All of the presented publications consider light-matter interactions and their potential application in atom interferometry, a comparatively young and rapidly evolving technique. Atom interferometers find application in high-precision measurements, the determination of physical constants, the testing of fundamental physics, and the provision of gravimeters and gyroscopes. The advancement of technology and science has led to significant improvements in performance and the development of ambitious mobile and space-based devices. The recent success of several experiments has led to the proposal of further experiments with the aim of opening up new frontiers. However, the construction of future devices necessitates a decision regarding the employed diffraction mechanism and geometry, depending on the specific technical and scientific requirements. Furthermore, it is necessary to enhance the sensitivity of future devices. The contributions in this dissertation address these issues. The first contribution (I) focuses on the diffraction of atoms by laser pulses which can be employed to generate atom-optical diffraction elements like beam splitters and mirrors. These diffraction elements can be combined to construct atom interferometers, which have been successfully employed for precision measurements regarding fundamental physics as well as practical applications. The article presents a numerical comparison of two distinct diffraction mechanisms (Bragg and Raman) and diffraction geometries (single and double diffraction) in microgravity. It discusses the fundamental differences between the mechanisms and geometries with respect to the diffraction efficiency, taking into account the width of the initial wave function and the duration of the light pulse. Additionally, it explores the transition between the two diffraction geometries when starting from an atom initially at rest and increasing its momentum. The results may serve as a reference for experimentalists in selecting the most suitable configuration, based on their aims and requirements in the realization of more advanced atom interferometers. The second contribution (II) is a follow-up to the previous one, but focuses exclusively on a single diffraction type in microgravity, namely the so-called double Raman diffraction. In contrast to the previous article, where we only discussed single two-photon processes, we consider in this article a six-photon process, also known as third-order diffraction, as well as three subsequent two-photon processes, which both lead to the same amount of transferred momentum and can both be used to realize large-momentum transfer (LMT). We demonstrate that third-order double Raman diffraction is a viable and advantageous method for the diffraction of small momentum distributions like Bose-Einstein condensates (BECs) compared to a sequence of three two-photon processes. Furthermore, we show that third-order Raman pulses can be successfully applied to create higher-order Raman atom interferometers. Third-order diffraction can be perfectly combined with other LMT techniques and, moreover, allows for a reduction in the overall duration of the diffraction process and the complexity of the experimental set-up, as only two distinct laser frequencies are required. Moreover, we present a third-order Mach-Zehnder interferometer with spurious paths being disregarded. As demonstrated later on in [3], this interferometer generates optimal contrast and a substantial amplitude. The third contribution (III) extends the semi-classical λ-scheme of single Raman diffraction, as discussed in detail in contribution (I), into a fully quantized multi-atom multi-λ configuration with center-of-mass motion inside a cavity. Therefore, the incorporation of an internal structure allows for a more realistic modeling of the atoms, which is relevant for multi-photon interaction or cooling processes. We use for our analysis the framework of second quantization, i.e., we take into account the field-theoretical nature of the multi-particle atomic field as well as of the diffracting light field. We reduce this model with a Hamiltonian averaging theory applied to the atomic field operators and obtain an effective Hamiltonian, which determines the time evolution of the system. We demonstrate the efficiency of our model by the application of a typical initial state. Moreover, for a specific input state, we obtain the Hong-Ou-Mandel effect simultaneously in the atomic and the optical system. Our many-body formalism is perfectly suited to theoretically describe contemporary high-precision atom interferometric experiments based on entanglement between the atoms, that aim to surpass the shot-noise limit.
The high-order intensity correlation function of N-photon interference with thermal light observed in a recent experiment [S. Oppel, T. B\"uttner, P. Kok, and J. von Zanthier, Phys. Rev. Lett. 109, 233603 (2012)] is analyzed. The terms in the expansion of the Nth-order correlation function are put into three groups. One group contributes a homogeneous background. Both of the other two contribute $(N\ensuremath{-}1)$-fold super-resolving fringes. In principle they correspond to coherent and incoherent superpositions of classical optical fields, respectively. Therefore similar super-resolving fringes can be obtained without intensity-correlation measurements. We report the experimental results of the coherent and incoherent super-resolving diffraction fringes, which are observed directly in the intensity distribution. The $N\ensuremath{-}1$ sources in both the coherent and incoherent cases are set in certain definite positions. In the coherent case, moreover, the phase difference between two adjacent source fields is $\ensuremath{\pi}$. The fringe visibility is unity in the incoherent case, while it decreases as N increases in the incoherent case.