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A. Dalafi

Publications and source records attributed to A. Dalafi.

At least 19 recordsLinked to original sources
arXiv2026

Effect of classical noises on the coherent population trapping based on the Green's function approach to the multiplicative stochastic processes

Inspired by the Green's function (GF) approach in quantum field theory (QFT) and many body physics, we have developed a mathematical formalism to investigate classical multiplicative stochastic processes. Based on this approach, the interacting GF of any dynamical system subjected to classical stochastic noises, which enter into the system equations of motion in a multiplicative way, can be obtained from the noninteracting (free of noise) GF through an infinite perturbative series which may converge to an exact closed form under special conditions. Using this formalism, we have studied the effects of classical noises of the driving laser on the coherent population trapping (CPT) which have a crucial role in the performance of CPT-based atomic clocks. We have shown that if the bandwidth of the colored noise is sufficiently larger than the system damping rate, the infinite series corresponding to the interacting GF can be approximated by the closed form. The presented formalism enables us to investigate all kinds of homogeneous and inhomogeneous broadening mechanisms on the CPT transmission resonance lineshape, including dephasing due to atomic collisions, power/Doppler broadenings, as well as the broadening mechanisms due to phase and amplitude fluctuations of driving laser and compared their destructive effect with each other. It should be emphasized that the presented formalism is applicable to any dynamical system with multiplicative stochastic noises and the CPT phenomenon is just a prototype for the application of the presented formalism in practice.

quant-ph↗
arXiv2025

Investigation of intrinsic nonlinear effects in driven-dissipative optomechanical systems using the generalized linear response theory

In this article, we study the effects of intrinsic nonlinear optomechanical interaction on the linear response of a driven-dissipative optomechanical system to a weak time-dependent perturbation. By calculating the linear response of the cavity optical mode to a weak probe laser in the framework of the generalized linear response theory, it is shown how the Stokes and anti-Stokes sideband amplitudes as well as the power reflection coefficient, and the density of states of the cavity optical mode are expressed in terms of photonic retarded Green's functions. Then, we derive the equations of motion of retarded Green's functions of the system from nonlinear quantum Langevin equations and solve them. It is shown that for a single-photon optomechanical coupling of the order of the cavity linewidth, the nonlinear effect does not manifest itself unless the system satisfies a resonance condition, where the frequency of the upper normal mode of the system is twice that of the lower one. Based on the generality of the present approach which works at all regimes, the validity of linearization approximation is also confirmed at the off-resonance regime.

quant-ph↗
arXiv2022

Homodyne coherent quantum noise cancellation in a hybrid optomechanical force sensor

In this paper, we propose an experimentally viable scheme to enhance the sensitivity of force detection in a hybrid optomechanical setup assisted by squeezed vacuum injection, beyond the standard quantum limit (SQL). The scheme is based on a combination of the coherent quantum noise cancellation (CQNC) strategy with a variational homodyne detection of the cavity output spectrum in which the phase of the local oscillator is optimized. In CQNC, realizing a negative-mass oscillator in the system leads to exact cancellation of the backaction noise from the mechanics due to destructive quantum interference. Squeezed vacuum injection enhances this cancellation and allows sub-SQL sensitivity to be reached in a wide frequency band and at much lower input laser powers. We show here that the adoption of variational homodyne readout enables us to enhance this noise cancellation up to $40 ~\mathrm{dB}$ compared to the standard case of detection of the optical output phase quadrature, leading to a remarkable force sensitivity of the order of $10^{-19} \mathrm{N}/\sqrt{\mathrm{Hz}}$, around 2-order enhancement compared to the standard case. Moreover, we show that at nonzero cavity detuning, the signal response can be amplified at a level three to five times larger than that in the standard case without variational homodyne readout, improving the signal-to-noise-ratio (SNR). Finally, the variational readout CQNC developed in this paper may be applied to other optomechanical-like platforms such as levitated systems and multimode optomechanical arrays or crystals as well as Josephson-based optomechanical systems.

quant-ph↗
arXiv2022

Negative cavity photon spectral function in an optomechanical system with two parametrically-driven mechanical modes

We propose an experimentally feasible optomechanical scheme to realize a negative cavity photon spectral function (CPSF) which is equivalent to a negative absorption. The system under consideration is an optomechanical system consisting of two mechanical (phononic) modes which are linearly coupled to a common cavity mode via the radiation pressure while parametrically driven through the coherent time-modulation of their spring coefficients. Using the equations of motion for the cavity retarded Green's function obtained in the framework of the generalized linear response theory, we show that in the red-detuned and weak-coupling regimes a frequency-dependent effective cavity damping rate (ECDR) corresponding to a negative CPSF can be realized by controlling the cooperativities and modulation parameters while the system still remains in the stable regime. Nevertheless, such a negativity which acts as an optomechanical gain never occurs in a standard (an unmodulated bare) cavity optomechanical system. Besides, we find that the presence of two modulated mechanical degrees of freedom provides more controllability over the magnitude and bandwidth of the negativity of CPSF, in comparison to the setup with a single modulated mechanical oscillator. Interestingly, the introduced negativity may open a new platform to realize an extraordinary (modified) optomechanically induced transparency (in which the input signal is amplified in the output) leading to a perfect tunable optomechanical filter with switchable bandwidth which can be used as an optical transistor.

quant-ph↗
arXiv2021

Dynamics of a hybrid optomechanical system in the framework of the generalized linear response theory

We present a theoretical study of the linear response of a driven-dissipative hybrid optomechanical system consisting of an interacting one-dimensional Bose-Einstein condensate (BEC) to an external time-dependent perturbation in the framework of the generalized linear response theory. Using the equations of motion of the open quantum system Green's function, we obtain the linear responses of the optical and atomic modes of the hybrid system and show how the atom-atom interaction of the BEC atoms affects the two normal resonances of the system as well as the anti-resonance frequency at which the optical field amplitude of the cavity becomes zero. Furthermore, an interpretation of the anti-resonance phenomenon is presented based on the the optical spectral density and the self-energy.

quant-ph↗
arXiv2021

A Green's function approach to the linear response of a driven dissipative optomechanical system

In this paper, we first try to shed light on the ambiguities that exist in the literature in the generalization of the standard linear response theory (LRT) which has been basically formulated for closed systems to the theory of open quantum systems in the Heisenberg picture. Then, we investigate the linear response of a driven-dissipative optomechanical system (OMS) to a weak time-dependent perturbation using the so-called generalized LRT. It is shown how the Green's function equations of motion of a standard OMS as an open quantum system can be obtained from the quantum Langevin equations (QLEs) in the Heisenberg picture. The obtained results explain a wealth of phenomena, including the anti-resonance, normal mode splitting and the optomechanically induced transparency (OMIT). Furthermore, the reason why the Stokes or anti-Stokes sidebands are amplified or attenuated in the red or blue detuning regimes is clearly explained which is in exact coincidence, especially in the weak-coupling regime, with the Raman-scattering picture.

quant-ph↗
arXiv2021

Ultra-precision quantum sensing and measurement based on nonlinear hybrid optomechanical systems containing ultracold atoms or atomic Bose-Einstein condensate

In this review, we study how a hybrid optomechanical system (OMS), in which a quantum micro- or nano-mechanical oscillator (MO) is coupled to the electromagnetic (EM) radiation pressure, consisting of an ensemble of ultracold atoms or an atomic Bose-Einstein condensate (BEC), can be used as an ultra precision quantum sensor for measuring very weak signals. As is well-known in any precise quantum measurement the competition between the shot noise (SN) and the backaction noise of measurement executes a limitation on the measurement precision which is the so-called standard quantum limit (SQL). In the case where the intensity of the signal is even lower than the SQL, one needs to perform an ultra precision quantum sensing to beat the SQL. For this purpose, we review three important methods for surpassing the SQL in a hybrid OMS: (i) the backaction evading measurement of a quantum nondemolition (QND) variable of the system, (ii) the coherent quantum backaction noise cancellation (CQNC), and (iii) the so-called parametric sensing, the simultaneous signal amplification and added noise suppression below the SQL. Furthermore, we have shown in this article for the first time how the classical fluctuation of the driving laser phase, the so-called laser phase noise (LPN), affects the power spectrum of the output optical field in a standard OMS and induces an additional impression noise which makes the total system noise increase above the SQL. Also, for the first time in this review it has been shown that in the standard OMSs, it is impossible to amplify signal while suppressing the noise below the SQL simultaneously.

quant-ph↗
arXiv2019

Back-action evading measurement of the collective mode of a Bose-Einstein condensate

In this paper, we investigate theoretically the back-action evading measurement of the collective mode of an interacting atomic Bose-Einstein condensate (BEC) trapped in an optical cavity which is driven coherently by a pump laser with a modulated amplitude. It is shown that for a specified kind of amplitude modulation of the driving laser, one can measure a generalized quadrature of the collective mode of the BEC indirectly through the output cavity field with a negligible backaction noise in the good-cavity limit. Nevertheless, the on-resonance added noise of measurement is suppressed below the standard quantum limit (SQL) even in the bad cavity limit. Moreover, the measurement precision can be controlled through the s-wave scattering frequency of atomic collisions.

quant-ph↗
arXiv2019

Force sensing in hybrid Bose-Einstein condensate optomechanics based on parametric amplification

In this paper, the scheme of a force sensor is proposed which has been composed of a hybrid optomechanical cavity containing an interacting cigar-shaped Bose-Einstein condensate (BEC) where the \textit{s}-wave scattering frequency of the BEC atoms as well as the spring coefficient of the cavity moving end-mirror (the mechanical oscillator) are parametrically modulated. It is shown that in the red-detuned regime and under the so-called impedance-matching condition, the mechanical response of the system to the input signal is enhanced substantially, which leads to the amplification of the weak input signal while the added noises of measurement (backaction noises) can be suppressed and lowered much below the standard quantum limit (SQL). In this way, such a hybrid system operates as an ultra-sensitive force sensor which can amplify the input signal and simultaneously suppress the added noises by controlling the amplitudes of modulation and the system cooperativities. The advantage of the presented nonlinear hybrid system accompanied with the mechanical and atomic modulations in comparison to the bare optomechanical cavities is the enhancement of signal amplification as well as the extension of amplification bandwidth.

quant-ph↗
arXiv2018

Strong quadrature squeezing and quantum amplification in a coupled Bose-Einstein condensate- optomechanical cavity via coherent modulation

We consider an optomechanical cavity with a movable end-mirror as a quantum mechanical oscillator (MO) containing an interacting cigar-shaped Bose-Eisenstein condensate (BEC). It is assumed that both the MO and the BEC interact with the radiation pressure of the cavity field in the red-detuned and weak coupling regimes while the two-body atomic collisions frequency of the BEC and the mechanical spring coefficient of the MO are coherently modulated. By analyzing the scattering matrix we find that a frequency-dependent squeezing is induced to the three subsystems only due to the coherent modulations. In the largely different cooperativities regime together with strong modulations, the mechanical mode of the MO and the Bogoliubov mode of the BEC exhibit quadrature squeezing which can surpass the so-called 3dB limit (up to 75 dB) with high robustness to the thermal noises. Surprisingly, in this regime by controlling the system and modulation parameters, a very high degree of squeezing (up to 16 dB) together with high purity of quantum state for the output cavity field is achievable. Furthermore, one can attain simultaneous strong quantum amplification, added-noise suppression, and controllable gain-bandwidth for the complementary quadratures of squeezed ones in the subsystems.

quant-ph↗
arXiv2018

Effects of quadratic coupling and squeezed vacuum injection in an optomechanical cavity assisted with a Bose-Einstein condensate

We investigate theoretically a hybrid system consisting of a Bose-Einstein condensate (BEC) trapped inside a laser driven membrane-in-the-middle optomechanical cavity assisted with squeezed vacuum injection whose moving membrane interacts both linearly and quadratically with the radiation pressure of the cavity. It is shown that such a hybrid system is very suitable for generating strong quadrature squeezing in the mechanical mode of the membrane and the Bogoliubov mode of the BEC in the unresolved sideband regime. More interestingly, by choosing a suitable sign for the quadratic optomechanical coupling (QOC) one can achieve a very high degree of squeezing in the mechanical mode and a strong entanglement between the mechanical and atomic modes without the necessity of using squeezed light injection. Furthermore, the QOC changes the effective oscillation frequencies of both the mechanical and the atomic modes and affects their relaxation times. It can also make the system switch form optical bistability to tristability

quant-ph↗
arXiv2017

Controllable generation of photons and phonons in a coupled BEC-optomechanical-cavity via the parametric dynamical Casimir effect

We theoretically propose and investigate a feasible experimental scheme for the realization of the dynamical Casimir effect (DCE) in a hybrid optomechanical cavity with a moving end mirror containing an interacting cigar-shaped Bose-Einstein condensate (BEC). We show that in the red-detuned regime of cavity optomechanics together with the weak optomechanical coupling limit by \textit{coherent} modulation of the \textit{s}-wave scattering frequency of the BEC and the mechanical spring coefficient of the mechanical oscillator (MO), the mechanical and atomic quantum vacuum fluctuations are parametrically amplified, which consequently lead to the generation of the mechanical/Bogoliubov-type Casimir phonons. Interestingly, in the coherent regime corresponding to the case of largely different optomechanical coupling strengths of the cavity field to the BEC and the MO, or equivalently largely different cooperativities, one can generate a large number of Casimir photons due to the amplification of the intracavity vacuum fluctuations \textit{induced} by the time modulations of the BEC and the MO. The number of generated Casimir particles are externally controllable by the cooperativities, and the modulation amplitudes of the atomic collisions rate and the mechanical spring coefficient.

quant-ph↗
arXiv2017

Controlling steady-state bipartite entanglements and quadrature squeezing in a membrane-in-the-middle optomechanical system with two Bose-Einstein condensates

We study theoretically a driven hybrid optomechanical system with a membrane-in-the-middle configuration containing two identical elongated cigar-shaped Bose-Einstein condensates (BECs) in each side of the membrane. In the weakly interacting regime, the BECs can be considered as single-mode oscillators in the Bogoliubov approximation which are coupled to the optical field through the radiation pressure interaction so that they behave as two quasi-membranes. We show that the degree of squeezing of each BEC and its entanglement with the moving membrane can be controlled by the \textit{s}-wave scattering frequency of the other one. Since the \textit{s}-wave frequency of each BEC depends on the transverse trapping frequency of the atoms which is an experimentally controllable parameter, one can control the entanglement and squeezing of each BEC through the trapping frequency of the other one.

quant-ph↗
arXiv2017

Intrinsic cross-Kerr nonlinearity in an optical cavity containing an interacting Bose-Einstein condensate

An interacting cigar-shaped Bose-Einstein condensate (BEC) inside a driven optical cavity exhibits an intrinsic cross-Kerr (CK) nonlinearity due to the interaction with the optical mode of the cavity. Although the CK coupling is much weaker than those of the radiation pressure and the atom-atom interactions, it can affect the bistability behavior of the system when the intensity of the laser pump is strong enough. On the other hand, there is a competition between the CK nonlinearity and the atom-atom interaction so that the latter can neutralize the effect of the former. Furthermore, the CK nonlinearity causes the effective frequency of the Bogoliubov mode of the BEC as well as the quantum fluctuations of the system to be increased by increasing the cavity driving rate. However, in the dispersive interaction regime the effect of the CK nonlinearity is negligible. In addition, we show that by increasing the \textit{s}-wave scattering frequency of atomic collisions one can generate a strong stationary quadrature squeezing in the Bogoliubov mode of the BEC.

quant-ph↗
arXiv2016

Dispersive interaction of a Bose-Einstein condensate with the movable mirror of an optomechanical cavity in the presence of the laser phase noise

We theoretically investigate the dispersive interaction of a Bose-Einstein condensate (BEC) trapped inside an optomechanical cavity with a moving end mirror in the presence of the laser phase noise (LPN) as well as the atomic collisions. We assume that the effective frequency of the optical mode is much greater than those of the mechanical and the Bogoliubov modes of the movable mirror and the BEC . In the adiabatic approximation where the damping rate of the cavity is faster than those of the other modes, the system behaves as an effective two-mode model in which the atomic and mechanical modes are coupled to each other through the mediation of the optical field by an effective coupling parameter. We show that in the effective two-mode model, the LPN appears as a classical stochastic pump term which drives the amplitude quadratures of the mechanical and the Bogoliubov modes. It is also shown that a strong stationary mirror-atom entanglement can be established just in the dispersive and Doppler regimes where the two modes come into resonance with each other and the effect of the LPN gets very low.

quant-ph↗
arXiv2016

Phase noise and squeezing spectra of the output field of an optical cavity containing an interacting Bose-Einstein condensate

We present a theoretical study of the phase noise, intensity and quadrature squeezing power spectra of the transmitted field of a driven optical cavity containing an interacting one-dimensional Bose-Einstein condensate. We show how the pattern of the output power spectrum of the cavity changes due to the nonlinear effect of atomic collisions. Furthermore, it is shown that due to a one-to-one correspondence between the splitting of the peaks in the phase noise power spectrum of the cavity output field and the \textit{s}-wave scattering frequency of the atom-atom interaction, one can measure the strength of interatomic interaction. Besides, we show how the atomic collisions affect the squeezing behavior of the output field.

quant-ph↗
arXiv2014

The effect of atomic collisions on the quantum phase transition of a Bose-Einstein condensate inside an optical cavity

In this paper, we investigate the effect of atomic collisions on the phase transition form the normal to the superradiant phase in a one-dimensional Bose-Einstein condensate (BEC) trapped inside an optical cavity. Specifically, we show that driving the atoms from the side of the cavity leads to the excitation of modes in the edges of the first Brillouin zone of every energy band, which results in the two-mode approximation of the BEC matter field in the limit of weak coupling regime. The nonlinear effect of atom-atom interaction shifts the threshold of the quantum phase transition of the BEC and also affect the power low behavior of quantum fluctuations in the total particle number. Besides, we show the possibility of controlling the quantum phase transition of the system through the s-wave scattering frequency when the the strength of the transverse pumping has been fixed.

cond-mat.quant-gas↗
arXiv2014

Squeezed-state generation via nonlinear atom-atom interaction in the atomic field of a Bose-Einstein condensate interacting with an optical cavity

In this paper, we investigate theoretically a system consisting of a one dimensional Bose-Einstein condensate trapped inside the optical lattice of an optical cavity. In the weak-interaction regime and under the Bogoliubov approximation, the wave function of the Bose-Einstein condensate can be described by a classical field (condensate mode) having some quantum fluctuations (the Bogoliubov mode) about the mean value. Such a system behaves as a so-called atomic parametric amplifier, similar to an optical parametric amplifier, where the condensate and the Bogoliubov modes play respectively, the roles of the pump field and the signal mode in the degenerate parametric amplifier and the s-wave scattering frequency of atom-atom interaction plays the role of the nonlinear gain parameter. We show that using the nonlinear effect of atomic collisions, how one can manipulate and control the state of the Bogoliubov mode and produce squeezed states.

quant-ph↗