NONLINEAR FREQUENCY CONVERSION IN A CRYSTALLINE WHISPERING-GALLERY MODE DISK

Transcription

1 NONLINEAR FREQUENCY CONVERSION IN A CRYSTALLINE WHISPERING-GALLERY MODE DISK Matt T. Simons College of William & Mary Abstract We are developing high quality factor whisperinggallery mode resonator (WGMR) disks for use in quantum information experiments. Our polished lithium niobate disks achieved a quality factors of Q > We observed the generation of λ = 532 nm through Type-I, noncritically phase matched second harmonic generation in our whispering-gallery mode resonator disk. Unexpectedly, we observed this second harmonic generation far from phase matching conditions (a difference of more than 100 C). The non-phase matched second harmonic was significant enough to produce stimulated Raman scattering at λ = 545 nm, 559 nm, 573 nm, and 587 nm. Figure 1: Heralded single photon generation. A randomly generated photon with frequency 2ω is downconverted to two photons, each with frequency ω, inside a nonlinear medium. As only two photons can be created, the detection of one heralds the presence of a single photon. Introduction Many quantum information applications require a method for storing quantum information. Reversible mapping of quantum states of photons into long-lived spin states of atoms based on electromagnetically-induced transparency (EIT) is a promising scheme for realizing quantum memory 1. While the possibility of light storage has been already demonstrated by many research groups, any practical application depends on development of a reliable source of on-demand single photons at the frequencies of atomic transitions and with a narrow bandwidth matching the spectral width of the EIT resonance. Alternatively, a continuous light field with nonclassical statistics (such as squeezed light or squeezed vacuum) can be used to transmit quantum information. Squeezing reduces the uncertainty in one quantum variable of a light field below the fundamental quantum limit at the expense of the the conjugated one. In addition to quantum information, squeezed light can be used to improve sensitivity of an interferometer, a necessary component of many modern technologies including advanced atomic clocks. Frequency conversion in nonlinear optical crystals can be used for both single photon production and the generation of squeezed light. Second harmonic generation (SHG) converts two photons of a strong continuous pump into a new photon at twice the frequency. If the pump is operated near the SHG threshold, then at random times two pump photons combine in the nonlinear medium to produce one single second harmonic (SH) photon. However, it is impossible to predict at what time this photon is emitted. In the reciprocal process - parametric down conversion (PDC) - one pump photon generates a pair of correlated photons. Detection of one of these photons signals (heralds) the presence of the other (Figure 1). This scheme is known as heralded single photon generation 2. These two processes are often used together to produce heralded single photons - a strong laser field at the fundamental frequency is up-converted in SHG to produce a pump-field for a down-converter that generates photon pairs at the fundamental frequency again. SHG can also produce squeezed light 3;4 : as the fundamental field is converted to the second harmonic field as it propagates through a nonlinear medium the fluctuations in both fields are attenuated (Figure 2). Simons 1

2 Figure 2: Squeezed light generation. Second harmonic generation is an intensity dependent process, such that high intensity fluctuations in the fundamental (ω) field are more often converted to the second harmonic (2ω) field than low intensity fluctuations. This reduces the intensity fluctuations in both fields, resulting in squeezed light. After propagation through the medium, both light fields are squeezed. These nonlinear interactions are well-known and often used in quantum optics; however, they require high laser power and very high quality cavities, which make these experiments expensive and rather involved. Additionally, the frequencies accessible through SHG and PDC processes are limited by the ability to reduce phase mismatch between the fundamental and harmonic fields, a result of the dispersion of the medium. Reducing this mismatch to zero (phase matching) optimizes the harmonic conversion. In second harmonic generation in a crystal, there is a momentum difference between the second harmonic (SH) and the fundamental fields, k = k 2ω 2k ω (Fig. 3). Non-zero ( k) leads to a phase mismatch, which limits the power build-up of the second harmonic field (Eq. 1). P 2ω Sin2 [ k L/2] ( k L/2) 2 (1) Methods for phase matching, in addition to increasing complexity, limit the frequencies obtainable from a given system. Without phase matching conditions, second harmonic generation is rarely detectable. Whispering gallery mode resonators (WMGRs) made from nonlinear crystals provide a nice alternative to traditional designs. The crystalline material of the resonator serves as a nonlinear medium, and the unique combination of high quality factors (Q-factors) and low mode volumes attainable in WGMRs 5 reduces the input power required for SHG. Their monolithic design has advantages over external mirrored cavities in terms of stability. However, the circular geometry of whispering gallery Figure 3: In the photon picture, second harmonic generation combines two photons of a lower energy field and creates a field with twice the frequency. Reducing the phase mismatch k to zero (phasematching) optimizes the conversion efficiency. Raman scattered fields are frequency-shifted by the absorption of phonons in the crystal. mode resonators further restricts the possible phase matching methods. While nonlinear WGMRs have been used to produce quasi-phase matched second harmonic generation 6 and recently naturally phase matched second harmonic generation 7, and optical parametric oscillation 8, the phase matching requirement still severely limits the range of frequencies that can be converted in a given material. In the past year, we have demonstrated considerable second harmonic generation in a crystalline whispering gallery mode LiNbO 3 disk far from natural phase matching conditions with modest pump power. Moreover, we observed the generation of four additional red-shifted fields through stimulated Raman scattering from our non-phase matched second harmonic field. WGMR Production Our whispering gallery mode resonators are disks cut from a birefringent uniaxial crystal, lithium niobate (LiNbO 3 ). The disks are 1mm thick with diameters of 7 mm 10 mm. We turn the disks on a lathe for shaping and polishing by hand. Sandpaper ( grit) is used to create curvature along the edge of the disk, and a progression of diamond sanding sheets (grain sizes from 30 µm to 0.1 µm) is used to achieve an optical quality polish (Figure 4). The quality of polish and curvature of the disk control the quality factor (Q-factor) 9 of the WGMR disk. The Q-factor is an important characteristic of a cavity as it is directly related to the lifetime of Simons 2

3 cavity, defined as F SR = Figure 4: Hand-polishing the rim of a LiNbO3 WGMR disk on a lathe. c nπd (2) characterizes the physical specifications of the disk. This is measured as the distance in frequency between adjacent modes. The full-width half max (FWHM) of the mode peaks measures the Q-factor of the disk ν (3) Q= F W HM where ν is frequency of the laser. Figure 5 shows the output from our best WGMR disk, with a Q This result is on par with previous results 6. Second Harmonic Generation a photon in the cavity. A WGMR with a higher Q-factor has a longer lifetime, allowing for greater power build-up and thus has a lower input power threshold for nonlinear effects. We have achieved 25/15 scratch/dig polish qualities on the rim of our disks, and thus have measured high Q-factors on the order of Q > 107. Generation of second harmonics requires that energy and momentum be conserved. The exchange of two fundamental photons for one SH photon ω + ω = 2ω satisfies the first condition. Momentum conservation requires a medium with an appropriate birefringence to satisfy k2ω 2kω = Excitation of WGMs The process of exciting whispering-gallery modes is similar to coupling light into a waveguide. A prism of a higher index of refraction than the WGMR disk is used to satisfy the coupling condition through frustrated total internal reflection (frustrated TIR) 10. By bringing the disk within the skin depth of the evanescent wave, light can enter the whispering-gallery modes of the disk. Light entering the disk is directed parallel to the edge of the disk, and undergoes total internal reflection as it travels around the circumference. It also scatters off of imperfections on the surface (left by polishing the edge). Currently the polish quality is the limiting factor for the Q-factors of our disks. The light in the disk is out-coupled through the same prism. The transmission of the out-coupled and reflected beam is detected as the frequency of the laser is scanned. Whispering-gallery modes are seen where there is missing transmission in the detected beam. This is the light that remains in (or is scattered out from) the WGMR disk. We coupled a λ = 795 nm (corresponding to the Rb D1 transition) diode laser scanned over a 10 GHz range into a lithium niobate disk of diameter d = 7.7mm. The free spectral range (FSR) of a 87 Simons 2ω (n(2ω) n(ω)) = 0 c (4) which, as described above, is the phase matching condition. For a particular fundamental frequency a crystal must have a birefringence that can compensate for the dispersion. There are several ways to tune the birefringence: angle phase matching (critical phase matching), quasi-phase matching, and temperature phase matching (noncritical phase matching). The circular geometry of the WGMR prohibits the use of critical phase matching. Quasiphase matching has been used in other WGMR experiments, where periodically-poled lithium niobate disk was polished and then used to produce frequency doubling at fundamental wavelengths of λ = 1.55 µm and µm 6. We have chosen to use the third method, which does not require a crystal to be periodically-poled. Since most nonlinear crystals birefringence depends on temperature on the order of 10 5 per C, there is only a small range of fundamental wavelengths that can support second harmonic generation. Though our ultimate goal is to produce nonclassical light at the 87 Rb D1 transition of 795 nm (for integration with a stored light experiment), we have not found a crystal capable of noncritical phase matching for this wavelength. We have been working at 1064 nm to continue our research until we discover a suitable crystal. A crystal s birefringence (and thus the wavelength range) is 3

4 Figure 5: Frequency scanned output (of a 795 nm laser) from our LiNbO 3 WGMR disk. FWHM of 36 MHz translates to a Q-factor of Q heavily dependent on the melt stoichiometry 11. We measured the phase matching temperature of two different wafers of lithium niobate (LiNbO 3 ), a negative uniaxial crystal, at λ = 1064 nm. Our congruent sample (ratio of lithium to niobium 0.95) achieved non-critical phase matching at T P M = 6 C, while our stoichiometric sample (Li/Nb 1) had a phase matching temperature of T P M = 140 C. In these cases the fundamental is polarized along the ordinary axis, and the second harmonic polarized along the extraordinary axis (also known as Type-I phase matching). Second Harmonic Generation in a Whispering-gallery Mode Resonator We mounted a polished stoichiometric LiNbO 3 disk in the setup shown in Figure 6. With an infrared λ f = 1.064µm fiber laser aligned to couple 25% into the disk, we covered and heated the system to 140 C. The input power of the laser was P 0 = 250 mw. Near T = 140 C, the phase matching condition was met inside the WGMR, and a green second harmonic (SH) field was generated at λ s = 532 nm (see Figure 7). We then improved coupling into the disk from 25% to > 70%, by adjusting the beam incidence angle and the focal lens to match the beam spot size with the whispering-gallery mode size at the prism-disk interface. This led to an unexpected result - the observation of SHG at room temperature, in a system with a phase matching temperature of 140 C. The SH was produced not only at room temperature, but a large range from 26 C 100 C. This non-phase matched, 532 nm second harmonic field was emitted out of the disk, collimated, and sent through a beam splitter to separate it from the 1064 nm fundamental field (Figure 6. The SH field was detected on a broadband spectrometer (Ocean Optics HR4000, resolution 0.4 nm), as shown in the top graph in Figure 8. The conversion efficiency was low compared to phase matched SHG 7 (we measured 3 µw from a 300 mw pump), but it was significant enough to produce additional nonlinear frequency conversion. Stimulated Raman Scattering The SH field inside the WGMR, produced from a pump power of 600 mw, was intense enough to generate stimulated Raman scattering. The new fields, generated at room temperature, were initially at λ = 545 nm and 559 nm (see middle graph in Figure 8). A higher 1064 nm input power (650 mw) lead to the generation of two more frequencies at λ = 573 nm and 587 nm (see bottom graph in Figure 8). These fields appear to be Raman-generated Stokes fields. They are collinear and polarized with the SH field. Raman scattering is an inelastic process whereby incident light (of frequency ω i ) is absorbed by a medium and then re-emitted at a shifted frequency ω s1 = ω i ± ω R. The energy difference corresponding to ω R is absorbed or lost by a phonon in the crystal (Fig. 3). Stokes fields result from Simons 4

5 Figure 6: The input 1064 nm laser is focussed onto a prism to couple into the whispering-gallery mode resonator (WGMR). Inside the WGMR a second harmonic (532 nm) field is produced. The polarizing beam splitter (PBS) separates the horizontally polarized 1064 nm beam from the vertically polarized 532 nm beam, which is then sent to a spectrometer (Spec.). Figure 8: Spectrum of transmission/emission from LiNbO 3 whispering-gallery mode resonator. Input was 1064 nm pump with powers from top to bottom: 11 mw, 600 mw, 650 mw. The insets show the region from 500 nm nm; labels show location of peaks in nm. Figure 7: Left: Diagram of coupling to a WGMR disk producing a second harmonic field. Right: Photo of an infrared 1064 nm laser coupled to a WGMR via prism, with green SHG produced inside the disk. Laser lines added to photo. a phonon created (+ω R ), anti-stokes fields from a phonon destroyed ( ω R ). In stimulated Raman scattering, the spontaneously scattered field propagating along with the incident field stimulates further scattering into the same field. This field builds up, and can undergo Raman scattering itself, creating a subsequent field with ω s2 = ω s1 ω R. The Stokes fields we observed were shifted from the SH field by λ 14 nm, corresponding to a wavenumber shift of k Raman = 455 ± 2 cm 1. Interestingly, no Stokes or anti-stokes sidebands were observed around the more powerful fundamental (1064 nm) field. Conclusions Whispering-gallery mode resonators offer potential for advancing the field of quantum information storage. We have shown that our WGMRs can achieve high quality factors (Q = 10 7 ), which make them particularly attractive for nonlinear frequency conversion. We demonstrated optical second harmonic generation (Figure 7) via Type-I noncritical phase matching in our stoichiometric LiNbO 3 WGMR disk. Through improving our apparatus, we unexpectedly observed significant non-phase matched second harmonic generation, which was independent of temperature. Moreover, the SH field in the WGMR disk was sufficient to generate stimulated Raman scattering at k Raman = 455 ± 2 cm 1. These emitted fields were centered at λ = 545 nm, 559 nm, 573 nm, and 587 nm. Achieving second harmonic generation in our WGMR disks will now allow us to begin producing squeezed light in both the fundamental and sec- Simons 5

6 ond harmonic fields. For implementation into an EIT-based light storage system, we must produce squeezed light at λ = 795 nm ( 87 Rb D1 transition). So far, we have been unable to find a crystal with appropriate properties for SHG at this wavelength. However, our observation of non-phase matched SHG indicates that we may be able to produce squeezed light at λ = 795 nm without regard to phase matching. Our subsequent work will investigate squeezing at both λ = 1064 nm and λ = 795 nm. The observed stimulated Raman scattering into yellow wavelengths may be useful as a source of CW light in the nm. Since this was produced from a non-phase matched SHG, WGMRs may also provide a source of CW lasing at frequencies that are typically difficult produce. Thanks to my advisors I. Novikova and E.E. Mikhailov. Thanks to David Gribbin for polishing WGMR disks. Special thanks to S. Aubin for the use of his lab space and laser. G. Leuchs, Naturally phase-matched secondharmonic generation in a whispering-gallerymode resonator, Phys. Rev. Lett., vol. 104, p , Apr [8] J. U. Fürst, D. V. Strekalov, D. Elser, A. Aiello, U. L. Andersen, C. Marquardt, and G. Leuchs, Low-threshold optical parametric oscillations in a whispering gallery mode resonator, Phys. Rev. Lett., vol. 105, p , Dec [9] L. M. et. al., Ultimate whispering gallery mode resonator and nontrivial relationship between spectrum and shape, Papers from The Conference on Lasers and Electro-Optics (CLEO) and the QELS, Long Beach, California, May [10] A. N. Oraevsky, Whispering-gallery waves, Quantum Electronics, vol. 32, no. 5, p. 377, [11] P. F. Bordui, R. G. Norwood, D. H. Jundt, and M. M. Fejer, Preparation and characterization of off-congruent lithium niobate, J. Appl. Phys., vol. 71, pp , Jan References [1] I. Novikova, N. B. Phillips, and A. V. Gorshkov, Optimal light storage with full pulse-shape control, Physical Review A, vol. 78, no. 2, p , [2] E. Knill, R. Laflamme, and G. J. Milburn, A scheme for efficient quantum computation with linear optics, Nature, vol. 409, pp , January [3] R.-D. Li and P. Kumar, Quantum-noise reduction in traveling-wave second-harmonic generation, Phys. Rev. A, vol. 49, pp , Mar [4] S. F. Pereira, M. Xiao, H. J. Kimble, and J. L. Hall, Generation of squeezed light by intracavity frequency doubling, Phys. Rev. A, vol. 38, pp , Nov [5] V. Braginsky, M. Gorodetsky, and V. Ilchenko, Quality-factor and nonlinear properties of optical whispering-gallery modes, Physics Letters A, vol. 137, no. 7-8, pp , [6] V. S. Ilchenko, A. A. Savchenkov, A. B. Matsko, and L. Maleki, Nonlinear optics and crystalline whispering gallery mode cavities, Phys. Rev. Lett., vol. 92, p , Jan [7] J. U. Fürst, D. V. Strekalov, D. Elser, M. Lassen, U. L. Andersen, C. Marquardt, and Simons 6