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Schematic representation of a single trapped atomic ion coupled to an nanoelectromecanical oscillator.
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An enduring challenge for contemporary physics is to experimentally observe and control quantum behavior in macroscopic systems. We show that a single trapped atomic ion could be used to probe the quantum nature of a mesoscopic mechanical oscillator precooled to 4K, and furthermore, to cool the oscillator with high efficiency to its quantum ground...
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... posses sensitivity of QEMS energy at the level of a single quanta, a detection which is very difficult with a simple linear coupling to displacement. Finally, we show that the ion-QEMS system can be configured to provide a very effective cooling mechanism for the mechanical oscillators [9] and estimate that it should be possible to cool a QEMS cantilever, precooled only to 4 Kelvin, to its ground state with very high efficiency. Here we describe a quantum model of a single trapped atomic ion which is electrostatically coupled to a very small doubly clamped cantilever, Fig. 1. This coupling can be switched on and off using an external bias voltage at an electrode on the oscillator. The ion is held in a mesoscopic micro-fabricated quadrupole Paul trap [12], and laser cooled using resolved sideband cooling [13]. External lasers are used to couple the internal electronic states of the ion to its vibrational degree of freedom. The bias gate on the oscillator carries a charge Q = C o V o ( t ) where C o is the capacitance of the gate. We allow for the possibility for the bias gate voltage V o ( t ) to be time dependent so that it may be set to zero to turn off the electrostatic coupling to the trapped ion. The ion carries charge + e . In the geometry of Fig. 1, the interaction energy between the ion and the oscillator is given by V c = keV o C o / | d + X ˆ ( t ) − x ( t ) | where d is the equilibrium separation of the oscillator centre of mass position and the ion. We set the equilibrium position of the ion at ...
Context 2
... posses sensitivity of QEMS energy at the level of a single quanta, a detection which is very difficult with a simple linear coupling to displacement. Finally, we show that the ion-QEMS system can be configured to provide a very effective cooling mechanism for the mechanical oscillators [9] and estimate that it should be possible to cool a QEMS cantilever, precooled only to 4 Kelvin, to its ground state with very high efficiency. Here we describe a quantum model of a single trapped atomic ion which is electrostatically coupled to a very small doubly clamped cantilever, Fig. 1. This coupling can be switched on and off using an external bias voltage at an electrode on the oscillator. The ion is held in a mesoscopic micro-fabricated quadrupole Paul trap [12], and laser cooled using resolved sideband cooling [13]. External lasers are used to couple the internal electronic states of the ion to its vibrational degree of freedom. The bias gate on the oscillator carries a charge Q = C o V o ( t ) where C o is the capacitance of the gate. We allow for the possibility for the bias gate voltage V o ( t ) to be time dependent so that it may be set to zero to turn off the electrostatic coupling to the trapped ion. The ion carries charge + e . In the geometry of Fig. 1, the interaction energy between the ion and the oscillator is given by V c = keV o C o / | d + X ˆ ( t ) − x ( t ) | where d is the equilibrium separation of the oscillator centre of mass position and the ion. We set the equilibrium position of the ion at ...
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Citations
... The driven single mode cavity along with Coulomb interaction is responsible for the levitation of nanosphere. The Coulomb interaction (coupling strength) can be realized by direct interaction between the charged on the nanosphere and the left cavity mirror and [34][35][36]. Coupling between the charged left cavity mirror and nanosphere can achieve the Coulomb interaction. This leads to a effective nonzero coupling between the nanosphere and the cavity [39]. ...
... 4Vc ε•−1 ε•+2 ω c , second term represents the interaction between the between the two cavity fields with hoping factor J and the last term denotes the Coulomb interaction between the nanosphere with charge Q 1 and the cavity mirror with charge Q 2 [34][35][36][37]. The two terms in H d represent the FIG. ...
In this paper, we analytically present the phenomena of nanomechanically induced transparency (NMIT) and transmission rate in a parity-time-symmetric ($\mathcal{PT}$-symmetric) opto-nanomechanical system (ONMS) where a levitated dielectric nanospheres is trapped near the antinodes closest to right mirror of passive cavity which further coupled to an active cavity via hoping factor. We find that the phenomenon of NMIT may be generated from the output probe field in the presence of an effective opto-nanomechanical coupling between the cavity field and the nanosphere, whose steady-state position is influenced by the Coulomb interaction between the cavity mirror and the nanosphere. In addition, the width and height of the transparency window can be controlled through the effective optomechanical coupling, which is readily adjusted by altering changing the nanosphere's radius and the Coulomb interaction. One of the most interesting result is the transition NMIT behavior in $\mathcal{PT}$-symmetric and broken $\mathcal{PT}$-symmetric regime. We show that the presence of nanosphere in the passive cavity enhances the width and transmission rate of NMIT window in passive-passive regime and in passive-active regime, a notable decrease of sideband amplification has been observed. These results show that our scheme may find some potential applications for optical signal processing an and quantum information processing.
... Here, our proposed hybrid quantum system can be carried out by photonic crystal cavity optomechanical systems, 57 electromechanical circuit systems, 82,83 waveguide-mediated distant mechanical coupling, 84 or the Coulomb interaction. 64,85,86 The phase-dependent phonon-phonon coupling can be achieved by coupling to a charge qubit in the electromechanical system 87 and has been demonstrated by two assistant cavities. 57 Furthermore, it was demonstrated that the phonon-phonon coupling between mechanical resonators can be controlled by gate voltage exerted on mechanical resonators in ion-nanomechanical systems, 43,88 where a gate voltage V(t) ¼ V 0 cos(ω ac t) with frequency ω ac is exerted on NRs by Ohmic contacts. ...
Hybrid spin-mechanical systems offer a promising platform for advancing quantum science and technology. However, practical implementation of applications within these hybrid quantum systems demands the seamless integration of supplementary physical components. In this context, we present a proposal for a multi-mode spin-mechanical setup, featuring the utilization of three-mode coupling nanomechanical carbon nanotube (CNT) resonators. These resonators interact with each other via a phase-dependent phonon-exchange mechanism, which is coupled to the same nitrogen vacancy (NV) centers in diamond. Based on the modulation of the phonon–phonon coupling phase and leveraging the triple Fano-like resonance phenomenon, a tripling of electromagnetically induced transparency (EIT) becomes achievable within the system. This tripling is accompanied by swift dispersion, leading to a subtle advancement or delay in outcomes. The phenomenon of triple Fano-like resonance, alongside the resulting triple EIT, engenders noteworthy slow-to-fast and fast-to-slow light effects, which is theoretically demonstrated in CNT resonators, with both identical and distinct frequencies. The findings underscore that CNT resonators with varying frequencies can evoke a more pronounced transition in the slow–fast–slow and fast–slow–fast light effects. This study lays the foundation for the application of phonon-mediated optical information storage and processing.
... The proposed hybrid quantum system can be carried out by photonic crystal cavity optomechanical systems, 65 electromechanical circuit systems, 60,91 waveguide-mediated distant mechanical coupling, 92 or the Coulomb interaction. [93][94][95] The phase-dependent phonon-phonon coupling, can be achieved by coupling to a charge qubit in electromechanical system 96 and has been demonstrated by two assistant cavity. 65 Furthermore, it was demonstrated that the phonon-phonon coupling between mechanical resonators can be controlled by gate voltage exerted on mechanical resonators in ion-nanomechanical systems, 50,97 where a gate voltage V ðtÞ = V 0 cosðu ac tÞ with frequency u ac is exerted on NRs by Ohmic contacts. ...
We theoretically propose a multiple-mode-coupling hybrid quantum system comprising two-mode-coupling nanomechanical carbon nanotube (CNT) resonators realized by a phase-dependent phonon-exchange interaction interacting with the same nitrogen-vacancy (NV) center in diamond. We investigate the coherent optical responses of the NV center under the condition of resonance and detuning. In particular, two-color electromagnetically induced transparency (EIT) can be achieved by controlling the system parameters and coupling regimes. Combining the spin-phonon interactions and phonon-phonon coupling with the modulation phase, the switching of one and two EIT windows has been demonstrated, which generates a light delay or advance. The slow-to-fast and fast-to-slow light transitions have been studied in different coupling regimes, and the switch between slow and fast light can be controlled periodically by tuning the modulation phase. The study can be applied to phonon-mediated optical information storage or information processing with spin qubits based on multiple-mode hybrid quantum systems.
... In our scheme, the electromechanical coupling rate can be significantly improved by DC driving the voltage in the LC circuit. The time-dependent bias voltage modulation for mechanical resonator has been realized experimentally [70]. Since we have demonstrated, when the mechanical and rf resonator have different frequencies, both the ground state cooling and quantum synchronization can be achieved by voltage modulation. ...
We explore the ground state cooling and quantum synchronization of the mechanical and low-frequency inductor-capacitor (LC) resonators in a hybrid three-mode optoelectromechanical system, in which the mechanical resonator is optically and capacitively coupled to the optical cavity and the LC circuit, respectively. We find that when the bias voltage modulation switch is incorporated into the direct current (DC) bias voltage, ground state cooling and quantum synchronization can be simultaneously achieved regardless of whether the mechanical resonator and the low-frequency LC resonator have the identical frequency. Furthermore, we elucidate the relationship between quantum synchronization and ground state cooling of the two resonators, that is, the simultaneous ground state cooling of the resonators must be accompanied by quantum synchronization. Our work may open up an alternative approach to the simultaneous ground state cooling and quantum synchronization of multiple resonators, which has fewer parametric limitations.
... We assume the distance between the two charged mechanical oscillators is much greater than the small oscillations of the charged mechanical oscillators ( q 1 , q 2 ≪ r 0 ) , the term describing the interaction between two charged mechanical oscillators can be expanded to the second order as 47 where the linear terms are absorbed in equilibrium positions, and quadratic terms are incorporated in the renormalization of oscillation frequencies. After omitting the constant term, the Coulomb interaction can be reduced to this form 48,49 where η = C 1 V 1 C 2 V 2 4πε 0 mω m r 3 0 is Coulomb coupling strength. The Hamiltonian of the system in a rotating frame at the frequency ω l takes the form www.nature.com/scientificreports/ ...
In this paper, we investigated the quantum correlation of nano-electro-optomechanical system enhanced by an optical parametric amplifier (OPA) and Coulomb-type interaction. In particular, we consider a hybrid system consisting of a cavity and two charged mechanical oscillators with an OPA, where the optical cavity mode is coupled with a charged mechanical oscillator via radiation pressure, and the two charged mechanical oscillators are coupled through a Coulomb interaction. We use logarithmic negativity to quantify quantum entanglement, and quantum discord to measure the quantumness correlation between the two mechanical oscillators. We characterize quantum steering using the steerability between the two mechanical oscillators. Our results show that the presence of OPA and strong Coulomb coupling enhances the quantum correlations between the two mechanical oscillators. In addition, Coulomb interactions are more prominent in quantum correlations. Besides, in the presence of OPA, the maximum amount of quantum entanglement, quantum steering, and quantum discord were achieved between the two mechanical oscillators is greater than in the absence of OPA. Moreover, a proper phase choice of the optical field driving the OPA enhances quantum correlations under suitable conditions. We obtain quantum entanglement confines quantum steering and quantum discord beyond entanglement. Furthermore, quantum entanglement, quantum steering, and quantum discord decrease rapidly with increasing temperature as a result of decoherence. In addition, quantum discord persists at higher temperature values, although the quantum entanglement between the systems also vanishes completely. Our proposed scheme enhances quantum correlation and proves robust against fluctuations in the bath environment. We believe that the present scheme of quantum correlation provides a promising platform for the realization of continuous variable quantum information processing.
... To ensure that the gravitational energy dominates over Casimir forces [48], the separation distance between the interacting objects needs to be sufficiently large, typically exceeding significantly the separation d 0 of the DWP [19]. We further take into account the mediator couples to the qubit via the direct spin-phonon magnetic coupling [49] and interacts with a nearby fixed mirror through the Coulomb interaction [42][43][44][50][51][52][53][54][55][56][57]. The Hamiltonian that describes such a system reads, ...
... As the term proportional to (± d0 2 − Xc) 2 is already very small under usual experimental conditions, we ignore all terms of order O ± d0 2 − Xc 3 . Similarly, in the case of Xc ≪ r 0 , H co can be expanded as [51,52,56] ...
Finding a feasible protocol for probing the quantum nature of gravity has been attracting an increasing amount of attention. In this manuscript, we propose a protocol to enhance the detection of gravitationally induced entanglement by exploiting the two-phonon drive in a hybrid quantum setup. We consider the setup consisting of a test particle in a double-well potential, a qubit and a quantum mediator. There is gravitational interaction between the test particle and the mediator, and a spin-phonon coupling between the mediator and the qubit. By introducing a two-phonon drive, the entanglement between the TP and the qubit are significantly enhanced and the entanglement generation rate is remarkably increased compared with the case without the two-phonon drive. Moreover, the entanglement between the TP and the qubit can be partially preserved in the presence of dephasing by the proposed strategy. This work would open a different avenue for experimental detection of the quantum nature of gravity, which could find applications in quantum information science.
... In addition, it has been theoretically predicted that the strong coupling regime of the anti-Stokes Brillouin interaction can be accessible in highly nonlinear waveguides [42,69]. The strong optomechanical interaction permits state swapping between photons and phonons [70,71] which is one way to achieve phonon cooling [72][73][74][75][76]. As a consequence, a Brillouin cooling scheme that can beat the phonon heating rate for continuous optomechanical systems coupled with the environment is highly desirable by manipulating the dynamics of photonic-phononic interaction in integrated waveguides. ...
Up until now, ground state cooling using optomechanical interaction is realized in the regime where optical dissipation is higher than mechanical dissipation. Here, we demonstrate that optomechanical ground state cooling in a continuous optomechanical system is possible by using backward Brillouin scattering while mechanical dissipation exceeds optical dissipation which is the common case in optical waveguides. The cooling is achieved in an anti-Stokes backward Brillouin process by modulating the intensity of the optomechanical coupling via a pulsed pump to suppress heating processes in the strong coupling regime. With such dynamic modulation, a significant cooling factor can be achieved, which can be several orders of magnitude lower than for the steady-state case. This modulation scheme can also be applied to Brillouin cooling generated by forward intermodal Brillouin scattering.
... Through the method in Refs. [36][37][38], Eq. (2) can be simplified to ...
... To study nonreciprocity, we dicuss the case of phase different θ = φ = π/2, then Eqs. (36), (37) can be simplified as ...
We theoretically propose a scheme of the nonreciprocal conversion device between photons of two arbitrary frequencies in a hybrid cavity optomechanical system, where two optical cavities and two microwave cavities are coupled to two different mechanical resonators via radiation pressure. Two mechanical resonators are coupled together via the Coulomb interaction. We study the nonreciprocal conversions between both the same and different types of frequency photons. The device is based on multichannel quantum interference to break the time-reversal symmetry. Our results show the perfect nonreciprocity conditions. By adjusting the Coulomb interaction and the phase differences, we find that the nonreciprocity can be modulated and even transformed into reciprocity. These results provide new insight into the design of nonreciprocal devices, including isolators, circulators, and routers in quantum information processing and quantum networks.
... The strong optomechanical interaction permits state swapping between photons and phonons [28,29] which is one way to achieve * Electronic address: birgit.stiller@mpl.mpg.de phonon cooling [30][31][32][33][34]. As a consequence, a Brillouin cooling scheme that can beat the phonon heating rate for continuous optomechanical systems coupled with the environment is highly desirable by manipulating the dynamics of photonic-phononic interaction in integrated waveguides. ...
In general, ground state cooling using optomechanical interaction is realized in the regime where optical dissipation is higher than mechanical dissipation. Here, we demonstrate that optomechanical ground state cooling in a continuous optomechanical system is possible by using backward Brillouin scattering while mechanical dissipation exceeds optical dissipation which is the common case in optical waveguides. The cooling is achieved in an anti-Stokes backward Brillouin process by modulating the intensity of the optomechanical coupling via a pulsed pump to suppress heating processes in the strong coupling regime. With such dynamic modulation, a cooling factor with several orders of magnitude can be realized, which breaks the steady-state cooling limit. This modulation scheme can also be applied to Brillouin cooling generated by forward intermodal Brillouin scattering.
... The last term represents the interaction between nanosphere and bath, where γ l is the coupling strength between nanosphere and the lth environmental oscillator. This kind of environment may be realized by the Coulomb force in quantum electromechanical system (QEMS) [66][67][68] or a high-reflectivity mirror fixed in the center of a doubly clamped beam in the cavity of optomechanical system [45]. The total Hamiltonian can be expressed by H = H s + H d + H e . ...
Nonreciprocity plays an indispensable role in quantum information transmission. We theoretically study the unidirectional amplification in the non-Markovian regime, in which a nanosphere surrounded by a structured bath is trapped in a single (dual)-mode cavity. The global mechanical response function of the nanosphere is markedly altered by the non-Markovian structured bath through shifting the effective frequency and magnifying the response function. Consequently, when there is a small difference in the transmission rate within the regime of Markovian, the unidirectional amplification is achieved in the super-Ohmic spectral environment. In the double-optomechanical coupling system, the phase difference between two optomechanical couplings can reverse the transmission direction. Meanwhile, the non-Markovian bath still can amplify the signal because of the XX-type coupling between nanosphere and its bath.
