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We study multiphoton blockade effects in a single-mode cavity interacting with two three-level atoms in $\Lambda$-configuration having position-dependent atom-field coupling. We consider the effects of dipole-dipole interaction (DDI) between the three-level atoms and show how the presence of DDI strongly influences the multiphoton blockade. For symmetric coupling of the atoms with the field, the DDI induces an asymmetry in the emission spectra as a function of pump field detuning. At positive detuning, the single-photon blockade gets stronger as a function of DDI strength, leading to photon antibunching. However, it becomes weaker at negative detuning and can also completely vanish. We show that this vanishing single-photon blockade is associated with a strong two-photon blockade, leading to two-photon bunching. Therefore, by just tuning the frequency of the pump field, we can achieve two very distinct features. We also study the effects of DDI when the atoms are asymmetrically coupled with the field and show that the proposed system exhibits two-photon bunching. We believe our results are important for the experimental realization of such systems where DDI may be present., Comment: 12 pages, 10 figures

We propose a method to enhance bipartite and tripartite entanglement in cavity magnomechanics using an optical parametric amplifier (OPA). We analyze this system and identified parametric regimes where different types of entanglement are enhanced. We show that a proper choice of the phase of the parametric amplifier leads to the enhancement of the bipartite entanglements. Moreover, the tripartite entanglement is also significantly enhanced in the presence of OPA. The OPA not only enhances the strength of entanglement but also increases the domain of entanglement over a wider space of detunings as compared to the system when no OPA is present. Similarly, the robustness of entanglement against temperature is also enhanced. Another important consequence of OPA is the fact that it relaxes the requirement of strong magnon-phonon coupling to generate cavity-magnon entanglement which is necessary for the case when OPA is not present. We believe that the presented scheme is a step forward to realize robust quantum entanglement using current technology., Comment: 8 pages, 7 figures

Zero-photon catalysis (ZPC) introduces noiseless attenuation and can be implemented by existing technologies in quantum key distribution (QKD) protocols. In this paper, we present a ZPC-based eight-state measurement-device-independent continuous-variable QKD (MDI-CV-QKD) combined with discrete modulation and reverse reconciliation. This ZPC-involved eight-state protocol shows better efficiency in terms of optimal modulation variances, secret key rates, transmission distances, tolerable excess noises, and reconciliation efficiency compared to the eight-state protocol without ZPC, the four-state protocol without ZPC, and the four-state protocol with ZPC, at a low signal-to-noise ratio (SNR)., Comment: 11 pages, 9 Figures

The observer-based feedback control for the two-level bilinear open stochastic quantum system is proposed in this paper. The state of open stochastic quantum system (OSQS) is described in the Cartesian coordinate system. The proposed state observer is designed by using state-dependent differential Riccati equation (SDDRE) and constructed for optimally estimating the state of OSQS from measurement output of the system. The state of observer is continuously updated by the output data of continuous weak measurement (CWM). A Lyapunov Feedback control is designed based on estimated state of the observer for the state transfer of OSQS. An exponential Lyapunov function is chosen to ensure the stability of the system. The observer-based Lyapunov feedback control (OLFC) strategy is developed according to the stochastic Lyapunov stability theorem. The numerical simulation results verify the achievability of the proposed OLFC strategy in terms of state estimation and state transfer of OSQS. Numerical simulations demonstrate that the observer tracks the state of system asymptotically with minimum error of ± 3%. The proposed OLFC has the ability to move the state of OSQS from arbitrary initial state to the final target eigenstate with high fidelity ≥ 90%.

Electromagnetically induced holographic imaging using strongly interacting Rydberg atoms is investigated via electromagnetically induced grating (EIG). We consider two schemes, i.e., by direct detection of holographic imaging pattern, known as electromagnetically induced classical holographic imaging (EICHI), and by employing entangled photon pairs for imaging which is called as electromagnetically induced quantum holographic imaging (EIQHI). Both schemes are employed to obtain 1D and 2D holographic imaging. In EICHI and EIQHI, amplitude and phase information of EIG can be imaged with controllable image variation in size. It is noticed that holographic imaging is influenced by van der Waals (vdW) effect present in Rydberg atoms.

We propose a scheme to study coherent control of the atomic Talbot effect using an N-type four-level atomic system in the Raman regime. We show that the intensity of the atomic Talbot image can be efficiently manipulated using Rabi frequency of the control field. However, this manipulation strongly depends on the proper choice of Raman and control field detunings. In particular, the sign of control field detuning leads to two distinct features. In one case, the intensity increases up to a maximum as a function of the control field, followed by a decreasing trend, while in other case, we find only a monotonically decreasing trend.

We consider the dynamics of the photon states in distant resonators coupled to a common bus resonator at different positions. The frequencies of distant resonators from a common bus resonator are equally detuned. These frequency detunings are kept larger than the coupling strengths of each resonator to the common bus resonator to satisfy the dispersive interaction regime. In the dispersive regime, we show that the time dynamics of the system evolve to an arbitrary W-type state in a single step at various interaction times. Our results show that a one-step generation of arbitrary W-type states can be achieved with high fidelity in a system of superconducting resonators., 11 pages, 8 figures, accepted

We have theoretically studied the electromagnetically induced grating (EIG) in a three-level \textbf{closed $\Lambda$-type atomic system}. The upper level is coupled to the two lower levels via a strong control and a weak probe \textbf{field}. In addition to these two optical fields a weak microwave field is also applied to couple the lower two levels. Our results show that the relative phase of the three fields \textbf{in the} presence of microwave field enhances the dispersion in the medium and consequently provides control over magnitude of the diffraction intensities. We \textbf{have optimized} the system parameters such as \textbf{strength of the fields} and interaction length to attain increased first order diffraction. Furthermore, we have also studied the effects of probe detuning on diffraction intensities. Interestingly, the probe detuning results in suppression of the zeroth order intensity while increasing the higher order intensities.

The rapid induction of Fiber Reinforced Plastics (FRP) into process industry due to high corrosion resistance and cost effectiveness made End Users to overlook FRP's specific design, fabrication and quality control aspects. This also affected various Utility and firewater networks in ADNOC Gas Processing plants. It is addressed by enhancing Vendor pre-qualification, relevant specifications and construction procedures. This paper presents measures adopted to ensure reliable design, supply and installation of FRP piping systems. FRP piping systems have unique design/construction requirements that was not followed in totality in AGP past installations. Also, international standards do not offer adequate guidance on design, resins selection, fabrication methods and joint systems. Vendors were trusted upon for complete design. A campaign is initiated to engage FRP pipe manufacturer having binding single point responsibility from beginning of project for particular FRP system design to ensure desired performance of FRP piping system with extended warranty. Measures have been taken to improve quality material supply through enhanced vendor pre-qualification, ADNOC Gas Processing specifications and CONTRACTORS pre-qualification having certified site crew. Studies revealed that material quality, velocity/surge pressure were the main contributing factors for failures which were not adequately addressed in design of FRP piping systems. Gaps noticed in previous projects were use of inadequate Codes, Composite's mechanical properties, design approach, inadequate joint preparation and QA/QC in construction phase. During manufacturing using wrong resin can be a cause for premature failure. Absence of certified personnel for project execution and Non-compliance of manufacturer's instructions were also key lapses noted in construction phase. The gaps in design process, necessitated improvement and consolidation of ADNOC Gas Processing existing design specifications/criteria and analysis requirements which now mandate that the required hydraulic / surge / static analysis shall be carried out by pre-qualified FRP manufacturer. Material property issues were addressed by clearly specifying the material composition & properties requirements and procedural requirements for storage are incorporated into the manufacturing process, along with mandating minimum prior experience for the manufacturers for material supply and design. Certification of contractor's personnel and presence of FRP manufacturer's representative at site during construction and pre-commissioning has been emphasized as mandatory requirement. In addition Specialist 3rd party inspection/supervision must be deployed to ensure quality control during every step of construction and commissioning Design specifications, procedures, manufacturing process, QA/QC and installation methods for FRP piping systems are available, but lacked activity interface between consultant, vendor and contractor. ADNOC Gas Processing enhanced the FRP specification ensuring single point responsibility with Vendor and procedures to ensure consistency from the design phase coherent with manufacturing process and appropriate implementation during the execution phase, in order to ensure the safety and integrity of FRP Piping systems.

This paper proposes a new Maximum Power Point Tracking (MPPT) technique for photovoltaic (PV) systems especially under Partial Shading (PS). This technique is based on Generalized Pattern Search (GPS) optimization algorithm. The proposed technique adopts the GPS algorithm owing to the reason that its major features like simple implementation, derivative free nature, fast convergence and high accuracy are ideally suited to deal with PS conditions. Furthermore, these features of GPS can well resolve the limitations and drawbacks of previous MPPT techniques, such as fluctuation, low efficiency, high complexity and slow convergence. For comparison, our proposed MPPT algorithm, the Particle Swarm Optimization (PSO) algorithm and the Perturb and Observe (P&O) algorithm have been implemented in MATLAB/Simulink. The comparison results demonstrate that the proposed MPPT technique can efficiently detect the global maximum (GM) in a fewer number of voltage samples, which is nearly 4 times less than the number of voltage samples required by PSO. Moreover, the steady state efficiency of the proposed MPPT is 99.8%, which is higher than the other MPPT techniques. Therefore, the proposed technique distinguishes itself from other MPPT techniques due to its superior quality in terms of convergence speed, dynamic and steady state efficiencies and low complexity.

We consider the resonant interaction of an ultracold two-level atom with an electromagnetic field inside a high- Q micromaser cavity. In particular, we study the tunneling and traversal of ultracold atoms through vacuum-induced potentials for secant hyperbolic square and sinusoidal cavity mode functions. The phase time which may be considered as an appropriate measure of the time required for the atoms to cross the cavity, significantly modifies with the change of cavity mode profile. For example, switching between the sub and superclassical behaviors in phase time can occur due to the mode function. Similarly, negative phase time appears for the transmission of the two-level atoms in both excited and ground states for secant hyperbolic square mode function which is in contrast to the mesa mode case.

Based on gain assisted electromagnetically induced transparency (EIT), we propose a scheme for coherent manipulation and storage of a microwave pulse propagating through a linear array of superconducting artificial atoms (SAAs). In an EIT-based system, the signal operates in an absorption mode, and its attenuation cannot be avoided during propagation. This results in low transmissivity of the medium. We show that based on gain assisted EIT, the attenuation can be ameliorated, and a probe pulse can be amplified while it propagates through the medium with significant reduction in its group velocity. The linear array of SAAs can thus act as a gain assisted EIT-based coherent microwave memory scheme with high fidelity.

In this paper, we study the atomic grating produced by a three-level ladder type system which interacts with a strong standing microwave drive field of finite bandwidth. The upper levels of the atoms are coupled by the drive field while the probe field is applied on the lower two levels. We find that in the presence of phase fluctuations associated with the microwave drive field, the diffraction intensities are significantly affected. Our results show that if the probe and microwave drive are on resonance with their respective atomic transitions, then the diffraction intensities can be improved by properly adjusting the strength of the drive field. However, if the probe field is detuned from the resonance, then the diffraction intensities can be improved by appropriately selecting the strength of the drive field, probe detuning and interaction length of the medium. Interestingly, our results also show that the effects of phase grating can also be enhanced by a pertinent choice of various parameters even in the presence of phase diffusion. This results in the suppression of the zeroth order intensity while the first order intensity is increased.

We study quantum state transfer and multipartite entanglement generation in the ensembles of qubits enclosed by a one-dimensional system of coupled optical cavities. Each cavity contains N qubits whose interaction with the quantum field of their respective cavity is governed by the Dicke Lipkin–Meshkov–Glick model. An excitation initially seeded in the ensemble at the end of the one-dimensional chain of coupled cavities transfers to the corresponding ensemble of the last cavity with success that depends on the mode-ensemble coupling χ , ensemble-mode detuning δ , photon hopping rate λ , and size of a given ensemble N . Suitable choices of such parameters enable overcoming the freezing effect induced by the choice of a far-off detuning regime. We identify working points at which three-ensemble W states and two-ensemble maximally entangled states emerge in the multipartite entanglement dynamics. This study provides a basis for manipulation of quantum states in a multipartite coupled cavity arrangement that may be useful in understanding very complex systems in the field of quantum information processing.

In this paper, we propose a scheme for the detection of weak magnetic field based on dissipatively coupled optomechanical system. The system considered here is composed of a perfect mirror and a compound mirror formed by a Michelson-Sagnac interferometer (MSI) with a movable membrane. When the transmissivity of MSI is close to zero, it sensitively depends upon the position of membrane. Under this condition, the two mirrors results in an effective Fabry-Perot interferometer (FPI) whose linewidth depends upon the position of the membrane. We show that by applying current to the membrane in the presence of magnetic field, the position of the membrane changes which in turn changes the linewidth of the effective FPI. This change can be observed in the spectrum of the output field and consequently enables us to measure weak magnetic field. Thus an optical detection technique is proposed for the detection of weak magnetic field.

In this paper, we study the effects of laser phase noise on the detection of a weak classical mechanical force on a free particle based upon dissipative optomechanical coupling. We show that for an optimum choice of various parameters, one can realize force sensing below the standard quantum limit even in the presence of laser phase noise. Moreover, we also investigate the effect of mechanical damping and thermal noise on force measurement in the presence of laser phase fluctuations. We show that force sensing strongly depends upon the phase fluctuations associated with the driving laser.

With focus on enhancing Integrity and efficiency, ADNOC Gas Processing identified an opportunity for optimization of existing FRP firewater system in Ruwais. A comprehensive study of complete firewater network and review of operating and control philosophy performed in order to optimize the system performance and mitigate pressure surge problems. This paper presents measures that ADNOC Gas Processing have adopted to achieve improved system efficiency and lower operating cost. A study was undertaken by GASCO to review issues with existing Fire Water network (FWN) at Ruwais to enhance overall performance of system in terms of design, operation and control. Initiative was to identify problems, evaluate root cause and think of optimization including some cost saving solutions. Study explored various operating configurations of existing 4-working+ 4-standby pumps with active involvement of operation personnel followed by hydraulic and surge analysis with different operating scenarios. Study revealed reduction in flow, head and pressure to mitigate fire water piping surge problems. Study also engaged pump vendors to establish feasibility of modifying the existing pumps. The study identified that each existing fire water pump is suitable to deliver 1400 m3/hr against required flow of 1000 m3/hr. Additional flow may create pressure spikes and surges in FWN. Hydraulic analysis found that pressure was above minimum requirement of 7bar (g) at the most remote point in network. Simulation indicated that fluid velocity was above 3.5 m/s at specific sections on the ring main. Increase in pipe sizes is required to arrest velocity within recommended limit in these areas. Option of lowering the operating pressure of main fire water pumps without the fire water network pressure falling below 7bar (g) at the most hydraulically remote point in the network was studied. Also the option of 3W+3S and 4W+4S [working (W) and standby(S)] pumping configuration was studied so as to establish that system can work with less number of pumps. Hydraulic study concluded that rated pressure should be reduced along with shut-off pressure. The maximum worst case fire water demand is 3200 m3/hr. The demand is found to be achieved with three Fire Water Pumps. During study pump vendors were engaged to arrive at the conclusion that 3W+3S configurations are hydraulically acceptable with pump / impeller modifications and de-staging options.

Based on phase controlled electromagnetically induced transparency, we propose a scheme for coherent control and storage of a microwave pulse in a linear array of artificial atoms. In particular, we consider the effects of the amplitude and phase of the fields driving the superconducting artificial atoms attached to a one-dimensional transmission line on the storage of a microwave pulse. We show that controlling the relative-phase of the microwave fields coupling the artificial atoms in a three-level Δ-configuration can yield tunable transparency window, which allows the propagation of a microwave pulse. The amplitude-control of the lower-levels coupling field adds a gain signature to the transparency window. Our results show that the absorption of the probe microwave pulse is suppressed and it gets amplified while propagating through an array of artificial atoms. The group velocity of the probe pulse is considerably reduced as a result atoms in a linear array act as coherent microwave memories.

The design of one qubit quantum gates with Lyapunov-based method is studied in this paper. Firstly, one qubit quantum control system is described in the coherence vector formation, then two types of Lyapunov functions are selected to implement NOT gate. The performances of control laws derived from both Lyapunov functions are compared and analyzed by means of the simulations for the NOT gate implementation.

We study the resonant tunneling of ultraslow atoms through a system of high quality microwave cavities. We find that the phase tunneling time across the two coupled cavities exhibits more frequent resonances as compared to the single cavity interaction. The increased resonances are instrumental in the display of an alternate sub and superclassical character of the tunneling time along the momentum axis with increasing energies of the incident slow atoms. Here, the intercavity separation appears as an additional controlling parameter of the system that provides an efficient control of the superclassical behavior of the phase tunneling time. Further, we find that the phase time characteristics through two cavity system has the combined features of the tunneling through a double barrier and a double well arrangements.

The objective of this paper is to design an adaptive proportional, integral, and derivative (APID) control strategy for a full car active suspension system. A nonlinear full car model is used to capture all the dynamics of a real vehicle suspension system. A vehicle’s stability and ride comfort is affected by road disturbances and can be improved by using an APID-based active suspension system. This paper presents performance assessment of the vehicle suspension system in terms of displacement and acceleration of seat, heave, pitch, and roll. The update parameters of APID are tuned online using the gradient descent method. The convergence of the proposed technique is guaranteed in the closed-loop control system. Simulation results show that the APID control scheme improves the convergence speed and robustness of the APID control strategy significantly for an active suspension system.

In this paper, a Lyapunov-based feedback control (LFC) is proposed for the state transfer of a two-level stochastic quantum system. The quantum state is described in the Cartesian coordinate system. An exponential function is selected as the Lyapunov function to ensure the stability of the system. The Lyapunov-based feedback control strategy is designed according to the stochastic Lyapunov stability theorem. Numerical simulations results show that the proposed LFC strategy has the ability to transfer the stochastic system from any initial mixed state to the desired eigenstate, and the LFC has high convergence rate and high state transfer fidelity.

We previously demonstrated that fragment based cat-SAR carcinogenesis models consisting solely of mutagenic or non-mutagenic carcinogens varied greatly in terms of their predictive accuracy. This led us to investigate how well the rat cancer cat-SAR model predicted mutagens and non-mutagens in their learning set. Four rat cancer cat-SAR models were developed: Complete Rat, Transgender Rat, Male Rat, and Female Rat, with leave-one-out (LOO) validation concordance values of 69%, 74%, 67%, and 73%, respectively. The mutagenic carcinogens produced concordance values in the range of 69–76% as compared to only 47–53% for non-mutagenic carcinogens. As a surrogate for mutagenicity comparisons between single site and multiple site carcinogen SAR models was analyzed. The LOO concordance values for models consisting of 1-site, 2-site, and 4+-site carcinogens were 66%, 71%, and 79%, respectively. As expected, the proportion of mutagens to non-mutagens also increased, rising from 54% for 1-site to 80% for 4+-site carcinogens. This study demonstrates that mutagenic chemicals, in both SAR learning sets and test sets, are influential in assessing model accuracy. This suggests that SAR models for carcinogens may require a two-step process in which mutagenicity is first determined before carcinogenicity can be accurately predicted.

Suspension system of a vehicle is used to minimize the effect of different road disturbances on ride comfort and to improve the vehicle control. The main objective of this work is to design an efficient active suspension control paradigm for full car model with 8 degrees of freedom using adaptive soft-computing techniques. The detailed mathematical model of the adaptive Mamdani fuzzy logic control and different adaptive neurofuzzy wavelet networks have been developed and successfully applied to a full car model. The parameters of the proposed controllers have been adjusted using online adaptation by minimizing the cost function. The robustness of the presented active controllers has been proved on the basis of different performance indices. Two road profiles have been used to check the performance of the proposed active suspension controllers as compared with passive, semi-active suspension, backstepping based fuzzy logic control, and linear quadratic regulated based suspension systems. The performance of the active suspension systems has been optimized in terms of displacement and acceleration of seat, heave, pitch, and roll.

A novel technique named Fuzzy-Like Adaptive Control (FLAC) is proposed for adaptive position control of a nonlinear dynamic plant such as the Induction Motor (IM). To accurately track the rotor position of an IM, the key has been a proper design of a controller. The proposed method utilizes the Modified Gaussian Radial Basis Function Neural Network (M-GRBFNN) for the learning of error. This scheme involves edge triggered standard deviation to update the centers and variances of the error. The major benefit of the proposed approach is ease along with excellent performance. It has been proved that the tracking error converges to the neighborhood of zero. The success of the proposed scheme is confirmed with the help of real-time experiments.

We present a scheme to realize electromagnetically induced grating in an ensemble of strongly interacting Rydberg atoms, which act as superatoms due to the dipole blockade mechanism. The ensemble of three-level cold Rydberg-dressed $(^{87}\mathrm{Rb})$ atoms follows a cascade configuration where a strong standing-wave control field and a weak probe pulse are employed. The diffraction intensity is influenced by the strength of the probe intensity, the control field strength, and the van der Waals (vdW) interaction. It is noticed that relatively large first-order diffraction can be obtained for low-input intensity with a small vdW shift and a strong control field. The scheme can be considered as an amicable solution to realize the atomic grating at the microscopic level, which can provide background- and dark-current-free diffraction.

Structure–activity relationship (SAR) models are powerful tools to investigate the mechanisms of action of chemical carcinogens and to predict the potential carcinogenicity of untested compounds. We describe the use of a traditional fragment-based SAR approach along with a new virtual ligand-protein interaction-based approach for modeling of nonmutagenic carcinogens. The ligand-based SAR models used descriptors derived from computationally calculated ligand-binding affinities for learning set agents to 5495 proteins. Two learning sets were developed. One set was from the Carcinogenic Potency Database, where chemicals tested for rat carcinogenesis along with Salmonella mutagenicity data were provided. The second was from Malacarne et al. who developed a learning set of nonalerting compounds based on rodent cancer bioassay data and Ashby’s structural alerts. When the rat cancer models were categorized based on mutagenicity, the traditional fragment model outperformed the ligand-based model. However, when the learning sets were composed solely of nonmutagenic or nonalerting carcinogens and noncarcinogens, the fragment model demonstrated a concordance of near 50%, whereas the ligand-based models demonstrated a concordance of 71% for nonmutagenic carcinogens and 74% for nonalerting carcinogens. Overall, these findings suggest that expert system analysis of virtual chemical protein interactions may be useful for developing predictive SAR models for nonmutagenic carcinogens. Moreover, a more practical approach for developing SAR models for carcinogenesis may include fragment-based models for chemicals testing positive for mutagenicity and ligand-based models for chemicals devoid of DNA reactivity.

In this paper, we discuss the effects of detuning on the velocity selection for ultracold three-level atoms in Λ configuration using mazer action. We find sharp resonances in the transmission probability with respect to the detuning. Our results show that the velocity selection of ultracold atoms can easily be tuned and enhanced using off-resonant field in a bimodal cavity.

In this paper, we propose a scheme for the teleportation of general two-partite entangled state of zero and one photon state from one bimodal cavity to another. The scheme can be realized by using cavity quantum electrodynamics (QED).

This proposal investigates the influence of the phase fluctuations on the time evolution of entanglement generation in a three-level correlated emission laser (CEL) with injected coherence. The atoms are injected in the cavity with an initial partial coherent superposition of the upper and lower levels. The corresponding phase φ is considered to be randomly distributed around some fixed phase φ 0 . The fluctuations in phase φ modifies the coherence between the two corresponding atomic levels. Therefore, we observe strong influence of phase fluctuations on the entanglement generation using the injected coherence CEL system.

In this paper, we discuss the velocity selection of ultracold three-level atoms in Λ configuration using a mazer. Our model is the same as discussed by Arun et al. [R. Arun, G.S. Agarwal, M.O. Scully, H. Walther, Phys. Rev. A 62 (2000) 023809] for mazer action in a bimodal cavity. We show that the initial Maxwellian velocity distribution of ultracold atoms can be narrowed due to the presence of resonances in the transmission through dressed-state potential. When the atoms are initially prepared in one of the two lower atomic states then significantly better velocity selectivity is obtained due to the presence of dark states.

A nanomechanical molecular “tape reader” is assembled and tested by threading a β-cyclodextrin ring onto a DNA oligomer and pulling it along with an AFM tip. The formation and mechanical operation of the system is confirmed by measuring the forces required to unfold secondary structures in the form of hairpins. Unfolding induced by this 0.7 nm aperture requires 40 times more force than that reported for pulling on the ends of the DNA. A kinetic analysis shows that much less strain is required to destabilize the double helix in this geometry. Consequently, much more force is required to provide the free energy needed for opening. DNA secondary structure may prove to be a significant obstacle both for enzymes that process DNA though an orifice, and for the passage through nanopores proposed for some novel sequencing schemes.

In this paper, we study the quantum phase properties of the field in a two-photon micromaser, including the effects of the finite detuning of the intermediate level. For initial coherent state of the cavity field and atoms initially in their excited state multipeak phase structure appears which eventually leads to the randomization of the cavity field phase. However, the approach towards the randomization depends upon the detuning. If the atoms are injected in a coherent superposition of their upper and lower atomic states then the phase distribution evolves into two-peak structure. For initial thermal state and atoms in polarized state, cavity field acquires some phase. We also consider the effect of finite Q of the cavity, random injection of the atoms and fluctuations in the interaction time.