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The following are not my beliefs, but a compilation of notes from conversations I had with a self-described Bitcoin “mutant”, named Edan Yago, contributor to Sovryn . Letting him ramble on about Bitcoin resulted in mesmerizing, mythical, and fascinating ruminations about Bitcoin’s destiny. So for one, I myself believe in Bitcoin as a digital store of value. It is a huge chunk of my portfolio, and I believe it will outlast 99% of the cryptocurrencies we have today. There is no better symbol of scarcity and hard money in crypto to date. However, I feel just about the same level of admiration for Ethereum, as it is opening up so many use cases through DeFi and DAOs. I am putting my biases aside to explain a very rare (and what I find fascinating) point of view. I present you Part 1 of The Hero’s Journey of Bitcoin: The Great Game The cryptocurrency experiment could not have higher stakes. Geopolitics is often referred to as the “Great Game”. It’s the game of thrones for global power. It is a game played by sovereign states. Bitcoin is the only way that ordinary people can play the Great Game. Bitcoin allows us to play this game by creating a sovereign currency that can challenge state powers and contend for the title of global reserve currency. To me that is the goal. For if we, ordinary people, can challenge sovereign states, we become sovereign ourselves: sovereign individuals. If we wish to play the game on this level, it is very important that we understand that this is a game that can only be played by Bitcoin. No other cryptocurrency can win this game, no matter how “advanced” it is. Indeed, if any other cryptocurrency ever seemed like it could rival Bitcoin for the mantle of Cryptocurrency King, it would not simply mean that Bitcoin had failed. The entire cryptocurrency experiment would have failed. The purpose of this is to explain why. First, we must examine the true nature of money. Then we must understand how Bitcoin hacked the nature of money to create the perfect money. Finally, we must understand Satoshi’s Paradox — that if anyone can create a successful crypto-”currency”, nobody can. Bitcoin is invented scarcity in the face of inflation The Homosapien: this weak, hairless, primate with pathetic teeth and claws, is the dominant life form on earth. How? It is not our intelligence, our ability to speak or our opposable thumbs. We had all those for hundreds of millenia and were still just in the middle of the food chain, living in fear of cats. So scared of bears it was . Then, just a few tens of millenia ago, something changed- and we began a rampage of domination across the planet. Intelligence and speech contributed, but the turning point was that we learned to collaborate at scale. We did this by creating shared illusions, “stories’’ that guided our behaviour beyond our tribal instincts and allowed us to share goals with people we may never meet, in distant lands and times. Chief among these shared illusions was religion and money. Religion allowed us to hold abstract ideals as collectively valuable. Money allowed us to trade with distant strangers, even adversaries. Blockchain is the newest human innovation for dispersed collaboration, even among adversaries, and it is no coincidence that it was invented for the express purpose of creating a super-money. taboo to even mention the word for bear Today, the dominant money, and hence the dominant shared illusion, is the US dollar. Despite the obvious flaws of fiat, there is no shared story as universally accepted as the U.S. dollar. USD is the current reserve currency of the world. are denominated in USD. People hide Benjamins under their mattresses in San Francisco, Beijing, Tehran, and Khartoum. No matter the differences in culture, political ideology, or religion, most of the world agrees on USD. Iran and the United States are in a state of open conflict. Yet, both hoard USD. It is the only cultural invention that is so universally accepted. 61% of international bank reserves To compete in the Great Game, we would need to create a shared story about money, that was the most powerful shared illusion yet. We would need to bewitch the world with a spell of almost unimaginable power. Ten years ago, Satoshi Nakamoto created that spell, wrote it in code, and unleashed it upon the world with the perfect Enochian ritual. What Satoshi Nakamoto did, should have been impossible. He created value from nothing. On January 3rd, 2009, the Bitcoin network came into existence and Satoshi Nakamoto mined the genesis block of Bitcoin. As of October 1, 2020, it sits at a market capitalization of about $200 Billion. Bitcoin has become a working manifestation of the abstract concept of financial sovereignty. Powerful as it is, his spell (like all magic) is a fragile illusion. “There are trivial truths and there are great truths. The opposite of a trivial truth is plainly false. The opposite of a great truth is also true.” ― Niels Bohr We must remember that shared illusions are just that: illusions. The greatest shared stories are mind-bogglingly absurd to the uninitiated. “Jesus was born to a virgin?” “Nirvana can only be achieved by ceasing to desire it?” “China is communist?” “USD has value?” The internal logic of Bitcoin is just as mind-warping. One need only listen to Warren Buffet as his mind reels from it: “Cryptocurrencies basically have no value,” said. “They don’t produce anything.” “It is a delusion, basically,” “ squared”. Buffett rat poison Buffet is not a stupid man. In fact, he is right, but he is not “right on the money.” Buffet sees only the trivial truth, not the great truth. What is the mind-warping great truth about Bitcoin? Bitcoin is an invented digital scarcity. Before Bitcoin was created, there was no shortage of Bitcoin, yet since it came into existence, the shortage of it only grows. And this is the fundamental truth that must be understood by anyone who seeks to understand cryptocurrency: It is valuable only if it is assuredly scarce. Without that fundamental property, the entire cryptocurrency spell is broken. , one of the most prominent new converts to the Church of Satoshi, explains this very clearly. When the Bitcoin forks began, he lost faith, the spell was broken. If anyone could create a “version of Bitcoin” — then Bitcoin’s scarcity was replaced with infinite inflation. He sold. Raoul Pal However, as Bitcoin triumphed against these pretenders, not only was his faith renewed, it was redoubled. Indeed, the threat that BCH, BSV and the other “competitors” represented, was a necessary step along Bitcoin’s hero’s journey to ultimate victory. Bitcoin is the invention of programmatic scarcity. It can only happen once. No blockchain after Bitcoin can invent programmatic scarcity again. Herein lies Satoshi’s Paradox: if anyone can create money through crypto-currency, then nobody can. Which brings me to ETH (and by extension, all altcoins) Anyone can create a token that has value. However, nobody can create a token that can be . And should any present or future Vitalik Buterin, Justin Sun or Gavin Wood, ever create a token that could plausibly rival Bitcoin, Bitcoin will fail. And with it, every single other pretender, including the token that came to rival Bitcoin, will also fail. money Before I explain why, let me be precise in what I mean by “fail”. I do not mean that Bitcoin will lose all value. Bitcoin will always have value, if only as a collectors item. What I mean by fail is that we will lose the Great Game. We will lose the ability to be sovereign through the creation of our own sovereign currency. We will lose the battle that really matters: the battle for the world’s premier money. Vitalik has always been very careful to describe ETH, not as a money, but as a commodity. ETH was analogous to oil, used to power transactions with “gas”. This was a very careful word choice by Vitalik, and I believe stems from an understanding of Satoshi’s Paradox. Recently however, the “ETH is money” meme has caught some traction. ETH, the argument goes, can “flippen” Bitcoin. ETH is the reserve currency of the Ethereum network, the Ethereum network is able to support advanced use-cases Bitcoin cannot, and this will lead to the Ethereum network overtaking the Bitcoin network and, as a result, to ETH overtaking BTC — and become the global Money. Perhaps you agree. Perhaps not. For our purposes here, it doesn’t matter. All you need to accept is that it is conceivable that altcoin could go through this process. We will use Ethereum merely as an example for why this logic is deeply flawed but also very important. some Imagine this wet dream of ETH-heads were to come to pass, what would happen? Bitcoin and Ethereum, would both — quickly or slowly — lose value. Why? For the simple reason that for all the Raoul Pal’s out there, the spell would be broken. Ethereum would prove that Bitcoin can be usurped but instead of capturing Bitcoin’s market capitalization, it would cap the potential market capitalization of both. Everyone would realize, including ETH-heads, that digital scarcity could be created by anyone with a big enough network, which would mean that Facebook, Tik Tok and the CCP could do it, which would then mean that they too could be usurped in the same way that tech companies regularly usurp each other. This realization would be followed moments later by the realization that digital scarcity can always be inflated, and therefore cannot exist. sustainably And with that the “exorbitant privilege” of Moneyness, that sustains the value of Bitcoin and the entire crypto-space would be gone. If anyone can do it, nobody can. All value would collapse to utility value, and since cryptocurrency can have near infinite velocity all value would tend toward zero. The entire space would experience what ICO tokens experienced in December 2017. A refutation of Chris Burniske’s that utility tokens can have sustainable value. Narrator: they can’t. misguided theory From MV = PQ to QED It is not enough for us to satisfy ourselves that Ethereum cannot succeed as Money. We must also look at the other side of the equation: it, or something like it, can destroy Bitcoin as a contender in the Great Game. I wish to grasp Satoshi’s Paradox in full. Only Bitcoin can be money… but also it is not guaranteed that Bitcoin will be money. If I may be pompous for a moment, I think that there is such a thing as enlightenment. I think that one achieves it by grasping that what one believes is a fragile illusion, while still having faith in the illusion. Buddah realized the illusion of self, without abandoning his ego. Niels Bohr realized the illusion of scientific theory, without becoming a flat earther. I invite you to realize the illusion of Bitcoin, without becoming a nocoiner. Here is where my thinking diverges from that of most Bitcoiners. Bitcoin can fail, but we cannot let it. We cannot let Ethereum, Ripple, Libra or any future challenger build a network effect to rival Bitcoin’s lest the fools ruin the party for themselves and all of us in their ignorant avarice. However, we must welcome challengers, for each new challenger strengthens Bitcoin, provided we defeat it. Yes, this is a space badger who happens to be bullish on Bitcoin As to how we can ensure that Bitcoin is never defeated, that the illusion never be revealed, I leave to you, dear listener. However, I will offer my own opinion. In the Bitcoin lore of old, there was once a meme, now seemingly forgotten: “Any technology which improves upon Bitcoin will simply be adopted by Bitcoin.” In the wake of the block-size wars, where any suggested change to Bitcoin became heresy, this meme was forgotten. The lesson of the Blocksize wars was well learned: don’t change Bitcoin. Bitcoin must remain inviolable. Let’s not learn the lesson too well though. Bitcoin should certainly adopt any technology which even might be valuable. The place to do this is in Bitcoin Layer2, and particularly on sidechains. Is Ethereum a technology “that improves upon Bitcoin”? Who cares, people seem to like it, and even find it useful. It is building network effects. “Yum”, says Bitcoin as it absorbs Ethereum’s powers- not on Bitcoin mainchain, but on the . “Fee Fi Fo Fum”, says Bitcoin, “do I smell more innovation?” Polkadot, you say? “Yum”, says Bitcoin, as it continues to snowball towards its destiny as Sovereign Money. Our Money. RSK sidechain Follow: Edan Yago on Twitter Sovryn on Twitter Sovryn Website Sovryn on Discord Sovryn Blog Ingamar on Twitter Also published at https://medium.com/sovryn/the-heros-journey-of-bitcoin-part-1-satoshi-s-paradox-64f90abb7811

Bitcoin: The Great Game

Raising Capital For Your Business: First Steps To a Great Deal

We are all at a wonderful ball where the champagne sparkles in every glass and soft laughter falls upon the summer air. We know, by the rules, that at some moment the Black Horseman will come shattering through the great terrace doors, wreaking vengeance and scattering the survivors. Those who leave early are saved, but the ball is so splendid no one wants to leave while there is still time, so that everyone keeps asking “What time is it? What time is it?” but none of the clocks have any hands — George J. W. Goodman, aka ‘Adam Smith’ Supermoney (1972) I obtained my financial independence during the Dotcom bubble of 1999. I was one of the lucky winners of that particular game. I never played in a financial bubble game before, and I never will again. I didn’t set out to play in a financial bubble game. I started a web site for home buyers back in April of 1994. A year later, I partnered with a relocation services firm. Until 1997, we tried to earn the most profit possible. Then, we were acquired by a large media company, which told us to concentrate on something called EBITDA, which is a measure of profits that does not deduct expansion costs. That is, we were encouraged to expand, but we remained fairly conservative. By 1999, other companies offering web-based relocation services were taking in venture capital and even going public. We saw that soon we would have to either try to go public ourselves or allow ourselves to be acquired by a company that already had issued shares on the stock market. All of us were skeptical of the market fascination with Dotcom stocks, so we took the conservative route and were acquired. That was a good choice, because by the time we could have put ourselves in shape to try to sell shares to the public, it would have been the summer of 2000, and by then the Dotcom bubble had popped. In fact, we were acquired by a company that I will refer to as BubbleDotCom, whose stock crashed while we were still locked out of selling it. Fortunately, our acquisition had not been paid for entirely with stock. Some of the proceeds were in the form of cash, and the cash retained its value. In short, a bunch of investors who bought shares in BubbleDotCom provided cash to that company, which used some of that cash to buy us. The investors, except for the few that might have sold early, eventually lost what they put in. Part of their loss became the source for my financial independence. Nothing to change my lifestyle, but enough so that I don’t have to get along with anyone to earn a living. The stock market and reality The stock market is not always in a bubble. Shares of stock give the holder part ownership in large companies. Ownership of a real company with real profits means that you have an asset with real value. Indeed, if you could predict accurately the profits of a company, then you could precisely calculate what share in its stock are worth. Future earnings are the reality on which stock market prices are based. But investors can disagree about where earnings are headed, so that some investors think that stocks are cheap while others think that stocks are expensive. As news plays out, some investors change their minds, and that leads to changes in share prices. Because future earnings cannot be known with certainty, you can never be sure that a market is in a bubble until after the fact. But Nobel Laureate Vernon Smith demonstrated thirty years ago that in an experimental stock market setting, even with future earnings known so that the correct value can be calculated, . bubbles frequently emerged Smith’s experiments showed that even when investors are aware that there is a discrepancy between stock prices and fundamental values, they continue to hold onto their shares and even buy more. I believe that what Smith found in experimental markets also can be found sometimes in the real world. When investors are aware that stock prices are high relative to traditional indicators of value, why do they not sell? I believe that the answer lies in the epigraph with which this essay began. Bullish investors have been earning paper profits and reaping psychic rewards, and they stick around in the hopes of more. They know that what Goodman calls the Black Horseman may come at any time to ruin the fun, but they presume that they can get out while their portfolios still show a profit. And yet it is mathematically impossible for all of the bullish investors to get out with a profit. If a stock goes from $10 a share to $100 a share and back down to $5 a share, then on average the shares bought on the way up have to be sold for less than their purchase price on the way down. If you buy into a bubble, then the chances are you will lose. A Bubble as a Chain Letter I believe that a bubble market acts a lot like a chain letter or pyramid scheme. A few people make a fortune in a bubble market, at the expense of a large number of people who take modest losses. The winners are those who sell close to the top, as we did with out Internet company. The losers are the many who buy on the way up and are unwilling or unable to get out before the crash takes place. Which brings me to Bitcoin. There are many people who will tell you that they have made money by being bullish on Bitcoin. But that is delusional. In order for people to realize their Bitcoin profits, they would have to sell, and if a lot of people sold, then that would have driven the price of Bitcoin down. Instead, it is a mathematical near-certainty that most people who believe that they have made large profits on Bitcoin are still holding most of their Bitcoin, so that their profits only exist on paper. And if Bitcoin crashes, which I expect it will, most of those people will not be willing or able to sell before their large paper profits have turned into small paper losses. Does that mean that going short Bitcoin is a sure bet? No. There is a saying, often attributed to John Maynard Keynes, that “the market can stay irrational longer than you can stay solvent.” This makes it perilous to try to fight a mania. If you saw the movie , or read the book, you know that if the market for mortgage securities had stayed irrational a few months longer, at least some of the bearish speculators would have been wiped out before their positions were vindicated. The Big Short But if I am correct that Bitcoin is a bubble, then somebody at some point can make a fortune by selling Bitcoin short, perhaps on the futures market that recently opened. The other big fortunes in Bitcoin will be made by the few who sell their Bitcoin while the the bulls still outnumber the bears. And once again, it is a mathematical near-certainty that most of the bulls will not get out in time. My advice is to stay away from playing the bubble game in financial markets. Let other people buy Bitcoin. Let other people short Bitcoin. Let other people buy stock market darlings like Amazon at extraordinary multiples of their recent earnings. Instead, invest in assets where the price has a more reasonable relationship to reality.

Playing the Financial Bubble Game

This paper is available on arxiv under CC 4.0 license. Authors: (1) Terence Blésin, Institute of Physics, Swiss Federal Institute of Technology Lausanne (EPFL) & Center of Quantum Science and Engineering (EPFL); (2) Wil Kao, Institute of Physics, Swiss Federal Institute of Technology Lausanne (EPFL) & Center of Quantum Science and Engineering (EPFL); (3) Anat Siddharth, Institute of Physics, Swiss Federal Institute of Technology Lausanne (EPFL) & Center of Quantum Science and Engineering (EPFL); (4) Alaina Attanasio, OxideMEMS lab, Purdue University; (5) Hao Tian, OxideMEMS lab, Purdue University; (6) Sunil A. Bhave, OxideMEMS lab, Purdue University; (7) Tobias J. Kippenberg, Institute of Physics, Swiss Federal Institute of Technology Lausanne (EPFL) & Center of Quantum Science and Engineering (EPFL). Table of Links Introduction Results A. Physics and design B. Device characterization C. Bidirectional microwave-optical transduction D. Pulsed transduction Discussion Acknowledgments Appendix A: Theory Appendix B: Fabrication process flow Appendix C: Optical characterization Appendix D: Characterization of acoustic resonances Appendix E: Characterization of bidirectional transduction Appendix F: Optimization of optical extraction efficiency Appendix A: Theory 1. Coupled mode theory for optical modes hybridization Using a pair of optical resonances increases the intracavity photon number for a given input optical power, resulting in an enhanced optomechanical interaction. Such an optical doublet is implemented here by evanescently coupling two micro-rings, forming a photonic molecule. Consider two bare optical modes with resonance frequencies ωl and ωr that correspond to the left and right micro-rings, respectively. The two modes couple with a rate J, which yields the Hamiltonian [1] and the equations of motion With Laplace transform, they can be rewritten in frequency domain as 2. Transducer Hamiltonian and input-output relations In terms of bare micro-ring modes, the transducer Hamiltonian is given by Note that the piezo-coupled acoustic mode interacts with only one of the micro-rings. To compute quantities directly related to the experiments, we rewrite the Hamiltonian in terms of the supermodes (Appendix A 1) as Finally, by defining effective optomechanical coupling rates and going into a rotating frame defined by the operator we have in the interaction picture. The time evolution of the bosonic modes can be computed using the Heisenberg-Langevin equations given by We can move to the frequency domain by using the Fourier transform along with the properties We then have 3. Conversion efficiency and added noise For the following analysis, we consider the triply resonant configuration where ω+ −ω− = ωm and the optical pump is on resonance with one of the optical supermodes. First, we consider the anti-Stokes configuration where ∆− = 0 and ∆+ = −ωm. From Eq. A24, we have the input-output relation The equations of motion is given by 4. Estimation of correlated microwave-optical pair generation rates Equations A40 and A43 suggest that entangled pairs of microwave and optical photons can be generated in the Stokes configuration since it gives rise to an effective two-mode squeezing Hamiltonian [3–5]. In order to verify that the HBAR transducer can generate entangled pairs of microwave and optical photons, we compute the on-chip pair generation rate, expected to be equal to the output photon flux from the lower frequency optical mode as in standard spontaneous parametric down-conversion (SPDC) scheme. Integrating over the transduction bandwidth, we have In practice, the pump laser should be filtered for the optical output to be dominated by heralding photons, and other losses from the measurement setup can further reduce the effective rate. For η oc = 7.9×10−5 , κ− = 2π×300 MHz and κm = 2π × 10 MHz, this would corresponds to an on-chip pair generation rate of 190 Hz. Losses in the measurement chain will have to be accounted for to estimate the count rate at the detector. In order to measure entanglement between the microwave and optical fields, the on-chip rate must be higher than the thermal decoherence rate of the acoustic mode κmnth,m(ωm), where the thermal occupancy nth,m(ωm) is given by the Bose-Einstein distribution. For ωm = 2π×3.5 GHz and κm = 2π×10 MHz, the decoherence rate at 800 mK is 43 MHz and 0.5 Hz at 10 mK. Therefore, the transducer needs to be operated in the mixing chamber of the dilution refrigerator, with a pulsed pump to reduce heat load. The total rate of optical heralding is hence gated by the pump duty cycle.

Bidirectional Microwave-optical Transduction Based on Integration: Appendix A: Theory

This paper is available on arxiv under CC 4.0 license. Authors: (1) Terence Blésin, Institute of Physics, Swiss Federal Institute of Technology Lausanne (EPFL) & Center of Quantum Science and Engineering (EPFL); (2) Wil Kao, Institute of Physics, Swiss Federal Institute of Technology Lausanne (EPFL) & Center of Quantum Science and Engineering (EPFL); (3) Anat Siddharth, Institute of Physics, Swiss Federal Institute of Technology Lausanne (EPFL) & Center of Quantum Science and Engineering (EPFL); (4) Alaina Attanasio, OxideMEMS lab, Purdue University; (5) Hao Tian, OxideMEMS lab, Purdue University; (6) Sunil A. Bhave, OxideMEMS lab, Purdue University; (7) Tobias J. Kippenberg, Institute of Physics, Swiss Federal Institute of Technology Lausanne (EPFL) & Center of Quantum Science and Engineering (EPFL). Table of Links Introduction Results A. Physics and design B. Device characterization C. Bidirectional microwave-optical transduction D. Pulsed transduction Discussion Acknowledgments Appendix A: Theory Appendix B: Fabrication process flow Appendix C: Optical characterization Appendix D: Characterization of acoustic resonances Appendix E: Characterization of bidirectional transduction Appendix F: Optimization of optical extraction efficiency III. DISCUSSION Non-classically correlated microwave-optical photon pairs can be generated through spontaneous parametric down-conversion in our transducer. These correlated photon pairs constitute a key ingredient toward entangling distant quantum processors via the Duan-LukinCirac-Zoller protocol [4, 45]. With the current device parameters, the pair generation rate on chip amounts to 190 Hz, which is well above the thermal decoherence rate for 3.5 GHz at 10 mK as explained in Appendix A 4. However, losses in the measurement setup specific to such an experiment, as well as the gating of the optical pump required to alleviate the effective heat load, are expected to limit further the final heralding rate. Quasi-free-standing structures, such as 1D OMCs, do not readily thermalize and are thus more susceptible to heating effects. Even though our transducer also utilizes a suspended acoustic resonator, it may be feasible to operate at a higher duty cycle than what is presented in Fig. 4. It has been shown that a buffer gas environment can facilitate thermalization of a 1D OMC, at the cost of increased damping of the mechanical breathing mode [46]. On the contrary, the HBAR mode of interest here should be relatively insensitive to such viscous damping, as the acoustic wave propagates predominantly along the longitudinal direction inside the cladding. Therefore, a sample cell affixed to the mixing chamber flange and filled with buffer superfluid helium—an inviscid fluid that is both an excellent thermal conductor and electrical insulator—could potentially improve the heralding rate without hampering the conversion efficiency [47]. The present design is also suited for tasks beyond quantum state transfer. The transducer can be a key component of photonic interconnects for superconducting qubits [7, 8], where laser lights routed through optical fibers are used to encode microwave signals directly inside the dilution refrigerator during qubit readout. It may be challenging for traveling-wave EOMs to attain the requisite half-wave voltage to be competitive in noise performance against conventional all-electrical readout scheme utilizing high-electron-mobility transistor amplifiers [8]. Our triply resonant approach affords a path towards a scalable optically controlled cryogenic waveform generator for both qubit readout and control. The multimode nature of the transducer is particularly suited for frequency-multiplexed dispersive readout. Transduction leveraging multiple HBAR modes is already demonstrated in Fig. 3e. One can additionally utilize line-type instead of point-type dimer coupling for the photonic molecule, which gives rise to a dispersion in the supermode splitting [48]. In combination with the multitude of acoustic overtones, a single transducer can therefore support several spectrally distinguishable triply resonant systems that serve as qubit multiplex channels. Finally, since the transducer requires no superconducting element to function, it may be pertinent for applications in classical microwave photonics. Optimization of design and fabrication should engender further improvement on device performance. The conversion efficiency, proportional to microwave extraction efficiency (Eq. 2), can be improved by replacing AlN with scandium-doped AlN [49], which features a piezoelectric coefficient d33 about five times larger than AlN [50, 51] while preserving CMOS compatibility. There is likewise additional upside on the photonics (Appendix C 1). Bending radiation loss can be significantly reduced by increasing the micro-ring radius r. In particular, intrinsic quality factor exceeding 107 has been demonstrated with an r approximately ten times larger using the same fabrication process [52]. It may be anticipated that the efficiency gain here may be chiefly compensated by the reduction in optomechanical coupling rate g0 ∼ 1/ √ r. Nevertheless, by thinning the waveguide to 200 nm that approaches half of the acoustic wavelength, g0 is expected to remain unchanged. As in the thick-core waveguide fabricated using the photonic Damascene process, such a thin-core waveguide on a subtractive manufacturing platform is expected to exhibit negligible bending loss [53]. Assuming critical coupling conditions (Appendix F), we therefore expect another 1.5- time gain in η tot. Finally, optical insertion loss can be nearly eliminated by employing a spot-size converter to facilitate mode-matching with lensed fiber [54–56]. Combining these improvements, our transducer could achieve a total efficiency η tot = 6 × 10−3 . In conclusion, we have designed, fabricated, and characterized a compact piezo-optomechanical microwaveoptical transducer that integrates wafer-scale, CMOScompatible HBAR and Si3N4 photonic technologies. Free of any superconducting components, this triply resonant transducer attains a bidirectional off-chip photon number conversion efficiency of 1.6 × 10−5 and a bandwidth of 25 MHz, with an input pump power of 21 dBm at room temperature. Multimode transduction leveraging distinct HBAR modes have been demonstrated, suggesting prospects for designing frequency-multiplexed photonic interconnects for superconducting qubits. Realistic design and fabrication improvements may even allow access to experiments in the quantum regime.

Bidirectional Microwave-optical Transduction Based on Integration: Discussion

This paper is available on arxiv under CC 4.0 license. Authors: (1) Terence Blésin, Institute of Physics, Swiss Federal Institute of Technology Lausanne (EPFL) & Center of Quantum Science and Engineering (EPFL); (2) Wil Kao, Institute of Physics, Swiss Federal Institute of Technology Lausanne (EPFL) & Center of Quantum Science and Engineering (EPFL); (3) Anat Siddharth, Institute of Physics, Swiss Federal Institute of Technology Lausanne (EPFL) & Center of Quantum Science and Engineering (EPFL); (4) Alaina Attanasio, OxideMEMS lab, Purdue University; (5) Hao Tian, OxideMEMS lab, Purdue University; (6) Sunil A. Bhave, OxideMEMS lab, Purdue University; (7) Tobias J. Kippenberg, Institute of Physics, Swiss Federal Institute of Technology Lausanne (EPFL) & Center of Quantum Science and Engineering (EPFL). Table of Links Introduction Results A. Physics and design B. Device characterization C. Bidirectional microwave-optical transduction D. Pulsed transduction Discussion Acknowledgments Appendix A: Theory Appendix B: Fabrication process flow Appendix C: Optical characterization Appendix D: Characterization of acoustic resonances Appendix E: Characterization of bidirectional transduction Appendix F: Optimization of optical extraction efficiency C. Bidirectional microwave-optical transduction We measure the off-chip efficiency η tot of the microwave-to-optical (up-conversion) and optical-tomicrowave (down-conversion) processes as a function of off-chip CW input optical pump power Pin. Compared to the on-chip efficiency η oc, this efficiency also accounts for the loss channels of the microwave and optical ports. First, we study the transducer in the triply resonant configuration. For up-conversion, the optical sideband generated from the microwave input, detuned by ωin = ωm from the pump frequency, is measured via a self-calibrated heterodyne detection method. The off-chip optical output containing both the pump (ωL) and the sideband (ωs) is combined with a local oscillator (LO; ωLO) and detected. By placing the LO at a frequency ωLO = (ωL + ωs) /2 + δ such that the photodetector response is constant over a frequency span of δ, we determine the sideband power relative to the pump. Picking off a fraction of the optical output then enables the determination of its absolute power and, by extension, that of the sideband with a power meter. The measured optical sideband power is compared to that of the microwave input to yield η tot. In the case of down-conversion, the optical input is generated by modulating the phase of the pump with an electrooptic modulator (EOM) driven by a microwave source of frequency ωEOM = ωm. Only one of the resulting sidebands is admitted into the photonic molecule and transduced, as the other is far off-resonance. The converted microwave power is directly probed with an electrical spectrum analyzer (ESA). Summarized in Figs. 3a and c, bidirectional transduction processes corresponding to both the effective beam-splitter (ωL = ω−; anti-Stokes) and two-mode-squeezing (ωL = ω+; Stokes) interactions are investigated. We reach a maximal η tot of −48 dB at 21 dBm pump for each configuration. Knowing the port losses, we estimate an on-chip efficiency η oc = −41 dB (Appendix E). Accounting for the extraction efficiency η ext, we further obtain an internal conversion efficiency η int = 2 × 10−3 from Eq. 2. Furthermore, we deviate from triple resonance to map out the transduction bandwidth. First, for a pump still resonant with one of the optical supermodes, the input microwave frequency ωin and input optical detuning (controlled by EOM drive frequency ωEOM) are varied for up- and down-conversion, respectively. Shown in Fig. 3b and d, transduction leveraging the main transduction mode exhibits a full width at half maximum (FWHM) of 25 MHz. The multimode nature of the transducer is further manifest in Fig. 3e, where the pump is in the beam-splitter configuration but slightly detuned from aˆ−. An additional transduction peak in η tot with a FWHM of 10 MHz is observed around ωin = 2π × 3.165 GHz, which corresponds to another HBAR one FSR away from the main transduction mode ωm = 2π × 3.480 GHz. The engineering degrees of freedom such as cladding and actuator thickness (HBAR FSR), and optical dispersion (supermode splitting as a function of optical wavelength) in the present system offer possibilities for frequencymultiplexed transduction.

Bidirectional Microwave-optical Transduction Based on Integration: C. Bidirectional

This paper is available on arxiv under CC 4.0 license. Authors: (1) Terence Blésin, Institute of Physics, Swiss Federal Institute of Technology Lausanne (EPFL) & Center of Quantum Science and Engineering (EPFL); (2) Wil Kao, Institute of Physics, Swiss Federal Institute of Technology Lausanne (EPFL) & Center of Quantum Science and Engineering (EPFL); (3) Anat Siddharth, Institute of Physics, Swiss Federal Institute of Technology Lausanne (EPFL) & Center of Quantum Science and Engineering (EPFL); (4) Alaina Attanasio, OxideMEMS lab, Purdue University; (5) Hao Tian, OxideMEMS lab, Purdue University; (6) Sunil A. Bhave, OxideMEMS lab, Purdue University; (7) Tobias J. Kippenberg, Institute of Physics, Swiss Federal Institute of Technology Lausanne (EPFL) & Center of Quantum Science and Engineering (EPFL). Table of Links Introduction Results A. Physics and design B. Device characterization C. Bidirectional microwave-optical transduction D. Pulsed transduction Discussion Acknowledgments Appendix A: Theory Appendix B: Fabrication process flow Appendix C: Optical characterization Appendix D: Characterization of acoustic resonances Appendix E: Characterization of bidirectional transduction Appendix F: Optimization of optical extraction efficiency B. Device characterization We perform metrological characterization to affirm the integrity of the stack. Shown in Fig. 2a, the region of suspended cladding is first identified through optical micrography; the released substrate below leads to a contrast in the image. To further access the layer structure, we use focused ion beam milling to create an opening on the device surface at the suspension site. This opening provides sufficient clearance to directly image the cladding acoustic resonator, pictured in Fig. 2b, confirming the removal of silicon. We then characterize the transducer as an optoelectronic network with one microwave port, two optical ports, and one auxiliary electrical DC port. Each optical port comprises an edge-coupled lensed fiber and on-chip bus waveguide terminated by 1D nanotapers designed for TE-polarized light, yielding a fiber-to-fiber coupling efficiency of −8 dB. For adjusting the frequency splitting between optical supermodes, a bias voltage is applied to the DC port to drive either the piezoelectric actuator [44] or an integrated thermo-optic heater placed in the vicinity of the micro-rings (Appendix C 2). The former affords no additional heat load and is hence cryogenic-compatible, whereas the latter provides an easy alternative for fast room-temperature characterization. The avoided mode crossing characteristic of a photonic molecule is exemplified in Fig. 2c. We access the HBARs through the microwave port. Calibrated high-frequency probes are used to contact the top and bottom electrode pads of the piezoelectric actuator, effectively linking the acoustic resonator with a transmission line. The reflection spectrum (Fig. 2d) reveals predominantly one single series of HBARs with a free spectral range (FSR) of 320 MHz, which corresponds to the acoustic length of the cladding. The transduction acoustic mode at 3.48 GHz exhibits a typical total linewidth of 13 MHz with a microwave extraction efficiency of κex,m/κm ≈ 11%. The microwave response is distinct from that of an identical stack composition with unreleased substrate. There, a periodic envelope corresponding to the cladding modes that are more strongly coupled to the microwave is superimposed over the full-stack HBAR response (Appendix D and Ref. [40]). The absence of these full-stack modes provide another piece of evidence of successful cladding suspension. Finally, we study the device acousto-optic response in the triply resonant configuration, where the transducer effectively operates as a resonant single-sideband modulator. The optical output containing both the pump at the symmetric-mode frequency and generated sideband at the antisymmetric-mode frequency are mixed by a photodetector. Such a beat-note spectrum shown in Fig. 2e displays response peaks aligned with the HBAR frequencies in Fig. 2d, demonstrating three-wave mixing.

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