We report the first experimental demonstration that two light pulses were made motionless and interacted with each other via a medium. The interaction time is, in principle, as long as possible and a considerable efficiency can be achieved even below single-photon level. We utilized the optical process of one photon pulse switched by another based on the effect of electromagnetically induced transparency to demonstrate the enhancement of optical nonlinear efficiency. With moving light pulses, the switching is activated at energy per area of 2 photons per atomic absorption cross section in the best situation as discussed in [Phys. Rev. Lett. 82, 4611 (1999)]. With motionless light pulses, we demonstrated that the switching is activated at 0.56 photons per atomic absorption cross section and that the light level can be further reduced by increasing the optical density of the medium. Our work enters a new regime of low light physics. Efficiency of a nonlinear optical process is equal to the product of transition rate and interaction time. Since the transition rate is dependent on the light intensity, a high intensity laser field is usually required in the nonlinear optics in order to achieve sufficient efficiency. On the other hand, if the interaction time can be made as long as possible, high efficiency can also be achieved even at low-light or single-photon level. With the techniques of light storage (LS) [1][2][3][4] and stationary light pulse (SLP) [5,6], we report the first experimental demonstration of enhanced nonlinear efficiency due to long interaction time between two motionless light pulses. In the LS, the storing process converts a light pulse to the ground-state coherence of an ensemble and the retrieving process vice versa. The LS provides a way to transfer quantum states between photons and atoms and can lead to the applications of quantum memory [7][8][9]. The SLP is created by the counter-propagating scheme of four-wave mixing. Unlike the stored light in the LS, an SLP maintains its electromagnetic component which is required for nonlinear optical interactions. Nevertheless, the formation of SLP was observed via the remaining energy released from the medium [5,6]. This work is also the first SLP application and provides the direct evidence of SLPs being electromagnetic fields in the medium. As SLPs significantly increase the interaction time between matter and light, they are very promising for applications in lowlight-level nonlinear optics [10] and studies in quantum many-body physics [11][12][13].As a proof-of-principle experiment, the nonlinear optical process that we considered is the all-optical switching (AOS) proposed by Ref. [14]. A weak probe and a strong coupling fields form the Λ-type configuration of electromagnetically induced transparency (EIT) [15, 16] * Electronic address: yu@phys.nthu.edu.tw and, hence, the absorption of the probe field is suppressed. The presence of a weak switching field enables the probe absorption owing to the third-order susceptibility [17,18]. If one photon ...

We demonstrate an efficient cross-phase modulation (XPM) based on a closed-loop double-Λ system. The property of the double-Λ medium can be controlled by changing the phases of the applied optical fields. This phase-dependent XPM scheme can achieve large phase modulations at low-light intensities without requiring cavities or tightly focusing of laser beams. With this scheme, we observe a π-level phase shift with two pulses both consisting of 8 photons in cold rubidium atoms. Such novel scheme provides a simple route to generate strong interactions between photons and may have potential applications in all-optical quantum signal processing.The realization of large cross-phase modulations (XPM) at low-light intensities, ultimately at the singlephoton level, is an important but challenging task in quantum information science [1][2][3]. To reach this goal, one often requires high-finesse cavities to enhance nonlinear interactions between photons [4,5]. However, cavitybased experiments require many compromises such as balancing cavity bandwidth and light-matter coupling strength, which remain technical difficulties. Another promising approach for generating strong photon-photon interaction is electromagnetically induced transparency (EIT) [6][7][8], but according to the theoretical predictions by Harris and coworkers, the cross-phase shift of the EITbased Kerr medium in free space has an upper limit of order 0.1 radians at the single-photon level [9]. To date, EIT-based XPM on the order of micro-radians per photon has been observed in cold atoms [10,11] and Rb-filled fiber system [12]. In recent years, to overcome this upper limit there have been many theoretical proposals and experimental studies on this subject including double slow-light schemes [13,14], stationary light schemes [15,16], cavity EIT schemes [17,18], or Rydberg EIT schemes [19][20][21][22][23][24]. Very recently, two research teams have overcame this upper limit and observed single-photon cross-phase shifts of π/3 and π by using cavity EIT [25] and Rydberg EIT [26], respectively. This is a great progress toward implementing a photonphoton gate.Here we report an experimental observation of a novel XPM scheme based on a phase-dependent double-Λ system. With this scheme, we observe a large cross-phase shift of 3.6±1.0 radians induced by a light pulse containing around 8 photons in cold rubidium atoms. This XPM scheme does not require cavities or Rydberg atoms, which provides a simple route to generate strong interactions between photons and obtain large cross-phase shifts per photon.In the present study, we investigate a closed-loop double-Λ XPM in a laser-cooled 87 Rb atomic system, as depicted in Fig. 1(a). Cold atomic gas with an optical depth of approximately 50 is produced in a dark spontaneous-force optical trap (SPOT) [27].A strong coupling field (Ω c denotes its Rabi frequency) drives the |2 ↔ |3 transition to create a transparent medium for a weak probe pulse (Ω p , |1 ↔ |3 ) through quantum interference. The coupling and probe fields form t...

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We observed electromagnetically-induced-transparency-based four-wave mixing (FWM) in the pulsed regime at low light levels. The FWM conversion efficiency of 3.8(9)% was observed in a four-level system of cold 87Rb atoms using a driving laser pulse with a peak intensity of approximately 80 {\mu}W/cm^2, corresponding to an energy of approximately 60 photons per atomic cross section. Comparison between the experimental data and the theoretical predictions proposed by Harris and Hau [Phys. Rev. Lett. 82, 4611 (1999)] showed good agreement. Additionally, a high conversion efficiency of 46(2)% was demonstrated when applying this scheme using a driving laser intensity of approximately 1.8 mW/cm^2. According to our theoretical predictions, this FWM scheme can achieve a conversion efficiency of nearly 100% when using a dense medium with an optical depth of 500.Comment: 5 pages, 5 figure

This study proposes an actively controllable method for fabrication of polymer microlens arrays. Hexagonal arrays of ferrofluid droplets, which were utilized as the mother-mold masters for microlens molding, were generated by inducing the magnetic hydrodynamic instability under different magnetic fields. To fabricate numerous cavity molds for microlens array molding, we used the field-dependent shapes of the ferrofluid droplets to create different sized molds. For the fabricated microlens arrays, their field-dependent bottom areas, lens height, radii of curvature, and the fill-factor were discussed. Furthermore, performances of the microlenses, including the numerical aperture, focal length, and depth of field, were tested.Index Terms-Ferrofluid droplet, magnetic hydrodynamic instability, microlens array.