Electromagnetic properties of terbium gallium garnet at millikelvin temperatures and low photon energy Nikita Kostylev,1 Maxim Goryachev,1 Pavel Bushev,2 and Michael E. Tobar1, a) 1)ARC Centre of Excellence for Engineered Quantum Systems, School of Physics, University of Western Australia, 35 Stirling Highway, Crawley WA 6009, Australia 2)Experimentalphysik, Universit¨atdes Saarlandes, D-66123 Saarbr¨ucken,Germany (Dated: 6 March 2018) Electromagnetic properties of single crystal terbium gallium garnet (TGG) are characterised from room down to millikelvin temperatures using the whispering gallery mode method. Microwave spectroscopy is performed at low powers equivalent to a few photons in energy and conducted as functions of magnetic field and temperature. A phase transition is detected close to the temperature of 3.5 Kelvin. This is observed for multiple whispering gallery modes causing an abrupt negative frequency shift and a change in transmission due to extra losses in the new phase caused by a change in complex magnetic susceptibility. Quantum communication and information processing magneto-optical properties17,18, has also been realised, has experienced rapid growth in the recent years, insti- but was proven to be rather weak due to short absorption gated by significant advances in quantum technology. A lengths19. This is quite a usual occurrence, as an operat- lot of attention is currently drawn towards developing ing approach in one frequency band typically introduces discrete elements of quantum circuits with a prospect significant disadvantages in the other20. Nevertheless, re- of unifying them in a single Hybrid Quantum System cent work has shown that bidirectional microwave-optical (HQS)1 in the future. One of the main complications, photon conversion is possible in YIG21, although the con- slowing down progress in this field of research, is the no- version efficiency in such a system was rather low, only ticeable disconnect between the multitude of approaches on the order of 10−10. The search is therefore ongoing for in performing operations on quantum states and handling magnetic materials that exhibit low losses at both sides their storage and transfer. A typical issue is the fre- of the spectrum, which may be mediated by spins and/or quency range each of these subsystems is limited to. For electronic properties and could result in high conversion example, structures, such as superconducting qubits2{4, rates. It is especially important to estimate these quali- or spins coupled to waveguides5, allow for processing and ties at low temperatures and low excitation levels where storage of information with particularly high fidelity, but quantum information may be preserved. operate primarily at microwave wavelengths. Long-range In this work, we characterize the electromagnetic prop- transfer of qubits, on the other hand, is realised best over erties of Terbium Gallium Garnet (TGG) single crys- optical links. In order to bridge the gap between these tals at millikelvin temperatures and single photon levels regimes, a device capable of performing high-efficiency, by microwave spectroscopy. TGG, which has a chem- high-rate quantum frequency conversion is required. ical composition Tb3Ga5O12 and a cubic garnet struc- Translating quantum information between microwaves ture that forms a geometrically frustrated three dimen- and optics is carried out using a system that has ac- sional Hyperkagone lattice22, is quite popular for its ap- cessible energy states in both frequency domains. Sug- plications in optics23{25. Similar to YIG, it has a high gestions have been made to use quantum mechanical Verdet constant, resulting in a large magneto-optical ef- resonators6,7, spin-doped dielectric crystals, such as iron 8 9{12 fect, which increases substantially when the crystal is ions in sapphire , Er:YSO , electro-optical effects in cooled towards cryogenic temperatures26. As a conse- materials such as lithium niobate13 and NV-centres in 14 quence, this crystal is considered particularly effective as diamond . The performance of these devices depends a Faraday rotator and isolator in laser setups, especially strongly on material properties, where of primary con- due to its excellent thermal conductivity, low optical ab- cern is the coherent interaction of system photons, and sorption coefficient and high laser-damage threshold27. thus coupling strengths to both microwave and opti- Recent work has shown interesting results with optical cal cavities play a major role. It has recently been coupling to TGG using the inverse Faraday effect, ex- shown that with certain ferrimagnetic crystals, such as 28,29 arXiv:1702.04081v3 [cond-mat.mtrl-sci] 25 Jul 2017 citing magnetic resonances at terrahertz frequencies . yttrium iron garnet (YIG), it is possible to reach extreme In these experiments, it has also been found that opti- coupling rates, including ultra-strong15 and superstrong 16 cal pumping with femtosecond laser pulses can be used coupling , where the system losses become comparable to modify the magnetic state of Tb ions. Knowledge on to mode frequency and free spectral range of the cavity accessing these states in the microwave regime could be respectively. Optical coupling to YIG, known for its good potentially extremely beneficial in bridging the optical- microwave frequency gap for quantum conversion appli- cations. Notwithstanding, except for a limited number of studies on magnetic properties, such as field-induced a)Electronic mail: [email protected] antiferromagnetism30, and discovery of anisotropic ther- 2 mal conductivity, such as the phonon Hall effect31, di- cavity resonator assembly was thermally connected to a electric properties of this material at low temperatures 20mK stage of a dilution cryostat and subjected to a and microwave frequencies have not been thoroughly in- magnetic field of up to 7T in strength, generated by a vestigated. superconducting magnet. The sample was tested using a vector network analyzer in transmission, with the room temperature signal level reduced by a series of cryogenic attenuators (-40dB in total) and the output amplified with two 20dB low noise amplifiers with one thermalised to 4K and the other to room temperature. The field was excited using straight microwave antennae, coupling primarily to the WGH modes (classified as having the dominant B-field aligned along the z-axis of the cylin- der and E-field in the radial direction) in the cavity. An example of the WGM is given in Fig. 2. Transmission, S21 FIG. 1: 3D schematic showing the whispering gallery 14 mode cavity formed by loading a cylindrical TGG (A) crystal inside a cylindrical copper cavity. (IV) 12 (III) 10 ^z Detuning, GHz (II) 8 (I) 6 -0.5 0.5 1.5 2.5 12 (B) ^z 11 FIG. 2: Simulated field density for a WGM with 10 azimuthal mode number m = 3 and !0=2π = 8.84 GHz. Detuning, GHz As for the spectroscopy technique, the whispering gallery mode (WGM) approach was chosen. It is an ex- 9 tremely sensitive tool that has on many occasions been proven to generate accurate estimates of electromag- -0.2 0.0 0.2 0.4 0.6 netic characteristics of materials32 and identification of Magnetic Field, T ion impurities8,33,34, including detection of paramagnetic spin flip transitions down to less than a few parts per FIG. 3: Whispering gallery mode frequency response of trillion35. This method has also been used in discovering the TGG crystal as a function of the external magnetic various nonlinear effects due to spin interactions, such as field. A section of the plot (A), showing the low applied masing in a two-level system36 and four-wave mixing37. magnetic field behaviour, is magnified in (B) to reveal To investigate this material, a cylindrical crystal of the complex level crossing structure. The most TGG was obtained with dimensions 15 × 15 mm (D×H) prominent modes are labeled with indexes (I-IV) and and was mounted in a cylindrical cavity manufactured will be referred to in latter figures. out of oxygen free (OFHC) copper to realise a dielectric loaded WGM resonator. The sample was undoped, with The experimental data for the magnetic field sweep as only traces of natural impurities expected to be present a function of frequency detuning at the temperature of in the structure. The crystal was fixed in place by ther- 20mK are shown in Fig. 3 and Fig. 4. A complex inter- mally conductive copper mounts, inserted into a 1mm action structure is present in the vicinity of zero applied diameter bore in the middle of the crystal (Fig. 1). The field, with the mode frequencies experiencing a rapid re- 3 pulsion as the field strength increases. The near zero Erbium-doped YAG crystal33. region at these ultra-low temperatures is characterised The shifts in the WGM frequencies can be related to by the Tb3+ ion ensemble being in the antiferromagnetic the complex magnetic susceptibility of the material38: phase due to the significance of the spin-spin interaction between Tb3+ ions22. Very high magnetic field tunabil- δν ity reaching 100GHz/T can be seen in the small-scale χ0 = 2 ; (1) interaction regions around B = ±0:15T. At higher fields, pm?ν0 the Zeeman term prevails and the ensemble is effectively characterised by the paramagnetic phase. Also, the re- where pm? is the perpendicular magnetic filling fac- sponse is mirror symmetric around the zero field with no tor and δν is the frequency deviation of the mode in significant dependence on the measurement history, i.e. relation to the resonance frequency ν0, as determined implying no detectable hysteresis. for high B fields. Fig. 4(B) shows the real part of the magnetic susceptibility χ0 for a wide range of magnetic fields. A frequency-dependent, dispersive response can (A) be observed when the material is in the effectively para- 0 magnetic phase, with an approximately linear relation- ship between χ0 values of the most prominent modes, as highlighted in the figure’s inset.