Anderson pseudospin and Superradiant Superconductivity revisited

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Highlights

  • Light induced room temperature transient superconductivity is explaine.

  • ‘Superradiant Superconductivity’, a new Dicke like cooperative phenomenon is predicted.

  • Ebbesen Labs finding of Tc increase in K3C60 without light, is explained using Hepp-Lieb-Scharf effect.

  • Light induced crystallization of Kosterlitz–Thouless vortices is predicted (with P.W. Anderson).

Abstract

Using Anderson pseudospins (Anderson, 1958; Bardeen et al., 1957), I suggested in 2012 (Baskaran, 2012) superradiant superconductivity (SRSC) and related Dicke phenomena in bulk superconductors. It was a response to a report from Cavalleri’s lab (Kaiser et al., 2012; Fausti et al., 2011), of transient room temperature superconductivity in YBCO, when pumped by 20 THz laser pulses. In my minimal model, Anderson pseudospins in k-space in a bulk superconductor were coupled to single polariton mode. The model was adapted to the pseudogap normal state of YBCO to explain observed transient superconductivity. We also pointed out, possibility of other Dicke phenomena, (i) spontaneous superradiance above a critical polariton matter coupling, with no pumping, (ii) enhanced quantum entanglement near the critical coupling and (iii) superfluoresence. Here we revisit our early work. Recent discovery by Ebbesens group (Thomas et al., 2019) of large increase of superconducting Tc from 30 K to 45 K in K3C60 via specially designed plasmon–phonon-polariton mode, but with no external pumping seems to be in line with our early prediction. Relevance of SRSC to developments, including other superradiant matters and Higgs Spectroscopy is pointed out.

Introduction

Several notions that P.W. Anderson introduced over seven decades continue to reverberate in the field of quantum matter and beyond. One such notion is pseudospin in k-space in BCS superconductors [1], [2]. I used this notion in 2012 and developed a minimal model and theory [3] to understand a fascinating challenge and new light from Cavalleri’s group, of observation of transient superconductivity at room temperatures in YBCO, when pumped by pulses of 20 THz laser. Present article is a revisit to my work in 2012, that suggested a new phenomenon called superradiant superconductivity (SRSC).

It was also pleasing that SRSC connected Anderson and Dicke, longtime colleagues at Princeton. Dicke superradiance [4], a spontaneous emission of radiation with intensity N2 of N excited two level systems, follows from a model of N identical two level atoms coupled, nearly resonantly, to a long wavelength electromagnetic mode.

In our work [3], a minimal model and way to combine superconductivity and superradiance into superradiant superconductivity was suggested, on general grounds, as a key first step to understand mechanism of transient superconductivity. In our model a long wavelength single boson mode interacts with a collection of independent 2-level atoms located in k-space and creates a Dicke superradiance situation. Our 2-level systems in k-space were Anderson pseudo spins, but with a twist (Section 2.1).

In our SRSC model for the experimental observation, conduction electrons were coupled to a single phonon-polariton mode. Wave length of hybridized phonon mode is as large as sample size, since for 20 THz radiation, λ 150μm, which is comparable to or larger than the active volume of the superconductor in the experiment. The presence of necessary two level systems within a wave length of the mode, enabled derivation of effective Dicke model.

Having suggested the possibility of Dicke phenomenon in a superconductor, we attempted to find a mechanism for observed transient superconductivity in the pumped normal state. This key second step was not straight forward. Unlike the normal state of a BCS superconductor, the pseudogap phase of YBCO supports significantly enhanced local pairing correlations [5], [6], [7], [8], as evidenced by many studies. We incorporated this in our minimal model and discussed the possibility of SRSC in the room temperature normal state. It resulted in a stimulated transient superconductivity, when acted upon by femtosecond pulses of THz laser.

In a recent (2019) article Uemura [9] emphasizes the presence of preformed pairs (as in pseudogap phase or equivalently being close to BEC limit in the Uemura plot) as favorable condition for enhanced photo induced superconductivity, consistent with our suggestion in 2012.

Drawing inspiration from what was known about the Dicke model [10], [11], [12] we predicted three remarkable possibilities in our paper: (i) spontaneous superradiance, in the absence of pumping, above a critical coupling of polariton mode with electrons, (ii) enhanced quantum entanglement near the critical coupling and (iii) superfluorescence. Recent work shows that dark states in Dicke system also exhibit non-trivial entanglement structures [13].

In an important recent development Ebbesen and collaborators have reported [14] a striking enhancement of superconducting Tc in K3C60, from 30 K to 45 K, in the presence of a strong coupling to an engineered plasmon–phonon polariton mode, in the absence of external pumping. This is in line with our prediction [3] that when polariton electron coupling exceeds a critical value, spontaneous SRSC and consequent increase in Tc is possible.

In a private conversation in 2012 Anderson suggested that a consequence of SRSC mechanism will be a self organization of vortices and antivortices into a periodic lattice, rather than a liquid of bound vortiex-antivortex pairs, in the quasi 2D YBCO superconductor when pumped with suitable femtosecond THz laser pulses. We will visit this in Section 7.

It is important to mention that an early (1996) and insightful paper, which we were not aware of till recently, Littlewood and Zhu [15] proposed and developed theory of superradiant phenomena in bulk exciton condensates. A very recent theoretical work, superradiant quantum materials by Mazza and Georges [16] addresses exciton condensates.

In what follows we elaborate our earlier work, add clarifications and discuss related issues. First we mention earlier microwave induced novel phenomena  [17], [18], [19], [20], [21] in low Tc superconductors and an early theoretical prediction of laser induced high Tc superconductivity (Tc 102 K) by Kumar, Sinha and Shankar [22], [23], [24] in 1968 and 1973. Then we refer to developments since 2012, in the experimental [25], [26], [27], [28], [29], [30], [31], [32], [33], [34], [35], [36], [37], [38] and theoretical fronts [39], [40], [41], [42], [43], [44], [45], [46], [47], [48], [49], [50], [51], [52], [53], [54], [55], [56], [57], [58], [59], [60], [61], [62], [63], [64], [65], [66], [67], [68]. Possible connection to SRSC is apparent in some of the later developments. In Section 9 we point out that, recent developments in the field of Higgs Spectroscopy [69], [70], [71], [72], [73], [74], [75], [76], [77], [78], where Anderson pseudo spins and some of their excitations (Higgs mode) play significant role, need to be looked at in the light of our early SRSC.

Section snippets

Radiation coupled to a superconductor

The interaction of coherent microwave radiation and laser radiation with low Tc superconductors is a relatively old subject [17], [18], [19], [20], [21], [22], [23], [24]. Our proposal of SRSC may have relevance to some known earlier results. Exciting later developments in 2011–12 began with the experimental observation of transient superconductivity well above Tc, induced by certain femtosecond laser pulses, in stripe ordered LCO [79] and pseudo gap phase of YBCO [80]. A series of later work

Superradiance in superconductors

In what follows, we start with an ideal BCS superconductor and show how Dicke superradiance emerges, when wavelength of macroscopically occupied external single boson mode λ exceeds the sample size L. Then we adapt our theory and model to the normal state of the pseudogap phase of YBCO, and take into account large local pairing correlations present even at room temperature scales.

In our work we made the tacit assumption that there are relaxation processes which drain energy to heat bath and

Derivation of Dicke model for superradiant superconductivity

Now we show that, in the low energy approximation, AAtoms are selectively coupled to a single external boson mode; the single mode boson Hamiltonian is Hb=ħω0(bb+12). The electron boson interaction term has a remarkably simple form, because of the absence of any space dependence. The external Boson mode, with a long wave length (long compared to the size of the superconductor) essentially modulates the band dispersion of Bloch electrons inside the sample in a k-dependent fashion. It does not

Wavefunction of superradiant superconducting state

To understand the meaning of the superradiant quantum state in a superconductor, consider the Dicke Hamiltonian, with identical two level atoms in resonance with the boson mode, HD=ħω0(bb+12)+ħω02iσiz+gNi(bσi+bσi+)Here i denotes a two level atom and N, total number of two level atoms. As defined earlier, N is the number of excited two level atoms and Nb is the occupancy of our single Boson mode. For every value of Nt (= N + Nb) there is a unique ground state, a nodeless in phase

A minimal Dicke model for the Pseudogap normal state of YBCO

Having theoretically suggested the possibility of Dicke superradiance in a BCS system in a superconducting state, we addressed femtosecond laser induced transient superconductivity observed in Ref. [80] in the pseudogap normal state of certain cuprates. In the experiment a Cu-O bond stretching mode is resonantly excited by an 80 meV ( 20 THz) femtosecond laser. In view of the resonance, the laser pumps energy and transfers coherence to the infrared phonon mode. The electronic subsystem in turn

Pumped normal pseudogap phase and transient superconductivity

To understand how superradiance stimulates transient superconductivity in the pseudo gap phase, we have to go beyond our model Hamiltonian (Eq. (18)) and consider self consistent modification of um and vm’s. We suggested a feed back mechanism; qualitatively it is as follows.

As mentioned in the last section, the (m, -m) subspace close to Fermi level contain AAtoms with high probability. AAtoms are in ground and excited states, determined by temperature, in the pseudogap normal phase. When

Self organized vortex lattice

As mentioned earlier, after I presented to Anderson, my proposal of SRSC and how it explains the experimental observation in 2012, he thought about it briefly. He was quick to remark that there is likely to be a self organization of preexisting thermal vortices and antivortices into a vortex lattice. It was a reminder to me that fascinating self-organization in space and time are generic in pumped nonequilibrium states.

Our preliminary analysis [83] did point out the possibility of self

Superradiance without pumping: Hepp-Lieb-Scharf effect

Inspired by the early theoretical suggestions and experimental works Ebbesen’s group have recently reported [14] a remarkable enhancement of superconducting Tc of fullerite K3C60 from 30 K to 45 K, in the absence of external pumping. What is novel is that they hybridize surface plasmon of Ag substrate and the long wavelength phonon mode of the superconductor, via a specific polymeric matrix, by embedding YBCO particles of suitable size in the polymeric matrix.

While other explanations for this

Higgs spectroscopy and AAtoms

The experimental signatures of the Higgs mode was presented by Sooryakumar and Klein [69] in 1980, followed by a theory of Littlewood and Varma [70], [71]. In 2013 Higgs modes were excited and seen using pump probe experiments in superconducting NbN [72]. The theory of this new experiment that followed [73], [74] by Tsuji, Aoki and collaborators discusses the phenomenon in the language of the precession of the Anderson pseudo spins. There are also other works related to Higgs spectroscopy [75],

Transient superconductivity resonances in YBCO

In a very recent experiment, the frequency of THz radiation was tuned from few THz to several 100 THz and interesting resonances in the transient response was reported [34]. It is likely that some of the low frequency resonances are related to internal excitations of strongly bound Cooper (preformed) pairs in YBCO. In our 2012 paper we also pointed out the possibility of enhanced SRSC whenever the frequency of the mode coincides with excited Cooper pair bound states or equivalently excited

Superradiant quantum matters

It is interesting that the superradiance we talked about in a bulk superconductor in 2012 could occur in other system. As mentioned in the introductory section, an early and insightful work by Littlewood and Zhu [15] in 1996 studied superradiance in an excitonic insulator. Partly following this work and using refined theoretical analysis Mazza and Georges [16] have discussed a theory of superradiance in the excitonic insulators very recently.

A careful examination of our derivation of the Dicke

Discussion and conclusion

A remarkable finding that started in 2011 in stripe ordered LSCO has gone a long way, in sharpening transient superconductivity at and above room temperatures in YBCO. It is exciting that K3C60 and some organic superconductors have joined the team. Remarkably, transient superconductivity that lasted only for several picoseconds in earlier experiments, has been elevated into metastable superconductivity lasting for 10 nanoseconds or so in K3C60.

It will be very nice to probe experimentally

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgment

It is a pleasure to thank: N. Kumar, K.P. Sinha, R.K. Shankar and R. Nityananda for discussions on photoinduced superconductivity in early 1970s; P.W. Anderson and N.P. Ong for discussions in 2012; A. Cavalleri, S. Kaiser, B. Keimer and H. Takagi for discussions in 2012 and hospitality during a visit to Germany.

K.P. Sinha and N. Kumar, my mentors at the Indian Institute of Science, Bangalore, India, exposed me in early 70s to experimental reports on microwave induced enhancement of Tc and Jc in

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