
- Photonics Research
- Vol. 10, Issue 4, 989 (2022)
Abstract
1. Introduction
Non-classical light is widely studied for on-chip light sources in quantum applications such as quantum computing, quantum metrology, and quantum sensing [1,2]. Non-classical light with a single photon property [3], photon entanglement [4], or squeezing property [5–8] can be generated in cavity quantum electrodynamic systems with an emitter and a microcavity. When the interaction between the emitter and the cavity mode is stronger than the cavity loss and emitter decay, the light–matter interaction reaches the strong coupling regime [9], which can be utilized to produce non-classical light with single photon and squeezing properties. The mechanism of single photon generation is a “photon blockade,” that is, the excitation of the first photon will decrease the possibility of exciting the second photon [10,11]. Additionally, the squeezing property, denoting quantum light with reduced quantum noise, can also be achieved in the strong coupling regime [12].
To date, photonic cavities have achieved ultrahigh quality factors [11,13–17] or ultrasmall mode volumes [18–20]; thus the strong coupling regime can be reached [21,22] in various structures including photonic crystals (PhCs) [14,23–25], micropillar cavities [26–28], whisper-gallery-mode microresonators [29–31], and plasmonic cavities [18,19,32–34]. In the past decade, photonic cavities equipped with quantum dots have attracted much attention in on-chip applications. Particularly, single photon sources are widely studied in on-chip devices with high-quality-factor microcavities, where strong coupling induces the photon blockade, and the detuning between atom and field can modulate the single photon property [35–40]. However, the generation of squeezing light by strong coupling in photonic cavities has not been fully explored and needs further progress, especially in on-chip devices. It would benefit precise measurement for quantum metrology [1] and light sources for quantum computing [2]. People have used plasmonic cavities [41] and micropillar cavities [28] to improve squeezing properties [42] by suppressing shot noise. But in the above studies, non-classical light emission couples only to free space. Aiming for a more compact and versatile quantum network, more advances are still needed for the on-chip generation and modulation of squeezing light.
In the present work, we propose a hybrid PhC–plasmonic system for on-chip generation and modulation of non-classical light. Hybridization between the band edge of a PhC waveguide and surface plasmons produces a band-edge mode with strong light confinement and a narrow linewidth with 3 meV, which ensures strong coupling. Thus, squeezing light and single photon emission can be simultaneously produced in the hybrid system. Especially, the squeezing light property is sensitive to loss, so the suppressed decay in strong coupling is beneficial to the generation of squeezing light. The strongly confined field provided by the AgNP also contributes to enhancement of the brightness of non-classical light output. Modulation of non-classical light is conducted by tuning the resonance of the band-edge mode, which can be realized by such methods as temperature tuning and current tuning [43]. The second-order correlation function
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2. MODEL SETUP OF THE STRONGLY COUPLED PHOTONIC-CRYSTAL–PLASMONIC-EMITTER SYSTEM
Our proposed system contains a PhC waveguide, a silver nanoparticle (AgNP), and a two-level emitter [Fig. 1(a)]. In the PhC structure, a line defect is introduced by removing an entire row of air holes in a hexagonal lattice, which supports guided modes. The AgNP is buried in the PhC lattice region. The field coupling between the PhC and AgNP produces a band-edge mode, which can be clearly seen in the absorption spectrum of the AgNP [44] [Fig. 1(b)]. For the band-edge mode, the PhC waveguide intensely couples with the AgNP, possessing a very high local density of states at its band edge. Note that it is not necessary to set the AgNP in resonance to produce the band-edge mode. Actually, the resonances of a single AgNP without a PhC waveguide lie far away from the band edge (
Figure 1.(a) Schematic diagram of the strongly coupled photonic-crystal–plasmonic-emitter system. The inset depicts the electric field profile of the band-edge mode. (b) Calculated absorption spectrum of AgNP (orange solid curve), and transmission spectra of the system with AgNP (blue dashed curve) and without AgNP (green dotted curve). (c) Coupling strength
The photon–emitter interaction system is generally described by the Jaynes–Cummings model under dipole and rotating wave approximations [5]. The system Hamiltonian is expressed as
Figure 2.Generation of non-classical light with single photon and squeezing properties. (a) Energy-level diagram of the system.
To guarantee strong coupling between the emitter and the band-edge mode, we set up our system with the following parameters. The lattice period of the PhC waveguide
With the above parameters, we use commercial COMSOL software to simulate coefficients
3. GENERATION AND MODULATION OF NON-CLASSICAL LIGHT
With the strongly coupled photon–emitter system above, we obtain non-classical light with single photon and squeezing properties. As shown in Figs. 2(c) and 2(d), the second-order correlation function
It is non-Hermitian because of added imaginary dissipation terms in the frequency of the emitter and the band-edge mode. The atom–photon states are denoted as
The energy of dressed states
Figure 2(c) demonstrates the single photon with varying wavelengths of pump light. Here, we set the band-edge mode and the emitter in resonance (
The squeezing property is depicted in Fig. 2(d) with normal-ordered quadrature fluctuation
The results above can also be achieved in analytical solutions in low-excitation subspaces with no more than two quanta. It is reasonable when the pump is very weak compared to the decay of the band-edge mode (here,
It can be seen that the expression of
Next, we introduce the refractive index tuning to study further non-classical modulation in our system. Here, we change the refractive index of PhC materials near 3.45 so that the band-edge mode
Figure 3.(a) Calculated second-order correlation function
In Fig. 3(b), the squeezing property is measured by the minimum of normal-ordered quadrature fluctuation
Additionally, qubit–qubit entanglement can be achieved in our system. When a metallic nanoparticle acts as a mediation of the coupling between two emitters, the strong localized field around the nanoparticle can enhance the qubit–qubit entanglement in hybrid plasmonic–waveguide systems [58,59]. This situation may also be achieved when two emitters are located beside AgNP in our system under the more confined field.
4. TRANSMISSION OF NON-CLASSICAL LIGHT
The line defect enables fine guiding of transmitted light in our system, which provides a convenient channel for output of non-classical light. The fine transmission property has been reported in the weak and intermediate coupling regime when AgNP is located in the line defect region [44] with weakly confined field and larger decays. The total emission rate
Figure 4.(a) Schematic diagram of every part of the decay rates. (b) Coupling efficiency
Unidirectional transmission is needed for practical on-chip devices. The spin-locked transmission [61], stemming from the coupling between the transverse spin and a circularly polarized emitter, provides a method to realize such an effect. We use the directionality
5. POSSIBILITIES OF EXPERIMENTAL REALIZATIONS
We give some possibilities of experimental realizations of our system below. The material of a PhC waveguide can choose AlGaAs. Its refractive index at 695 nm is close to our settings (
6. Conclusion
We have theoretically proposed a strongly coupled PhC–plasmonic-emitter system to generate and modulate non-classical light. A strongly confined band-edge mode, which occurs at the band edges of PhCs and possesses a very narrow linewidth, is utilized to realize strong photon–emitter coupling. In such a condition, we have obtained simultaneous single photon and squeezing properties. Modulation of our system can be realized through varying pump frequencies and cavity–emitter detunings, which is feasible in experiments with temperature tuning [50]. The generated non-classical light can be well channeled by a PhC waveguide with high coupling efficiency and unidirectional propagation. The proposal extends the study of non-classical light sources in nanophotonic structures and provides a candidate for a versatile non-classical light source for on-chip applications.
APPENDIX A: DETAILS OF ELECTROMAGNETIC SIMULATION
The numerical simulation is conducted in a PhC waveguide module of 12 rows and 13 columns [Fig.
Figure 5.(a) Schematic diagram of calculation module of strongly coupled photonic-crystal–plasmonic-emitter system. The silver nanoparticle and the emitter are shown by a red circle and an arrow, respectively. (b) Cross section of the module. The PhC layer is between two air layers. (c) Integral region
The integral region
APPENDIX B: PROPERTIES OF THE PHOTON–emitter system under lower dipole moments
Under experimental conditions, the more common choice of the dipole moment of the emitter is lower than the setting in our system (
Figure 6.Output spectrum from the transmitted photon
APPENDIX C: ANALYTICAL RESULTS OF THE PHOTON–emitter System
Below are details of analytical results of coefficients
The steady-state solutions of the system (
The eigenenergies of dressed states
The second-order correlation function
In the expressions above, terms with orders higher than
APPENDIX D: FURTHER DETAILS OF NON-CLASSICAL LIGHT PROPERTIES
We show further details of non-classical light properties. The state populations are depicted in Fig.
Figure 7.(a), (b)
Figure 8.
Next, the relation between photon bunching and squeezing is clarified. We choose two typical cases in Fig.
It is worth mentioning that only a conventional blockade occurs in our system. It can be verified by the fact that every minimum of
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