Mezbon–mehmon kristall muhandisligi spin tashuvchi mehmon molekulani turli kristall mezbonlarga nazoratli ravishda joylashtirish orqali mahalliy tebranish, molekulyar joylashuv va yadro-spin muhitini oʻzgartirish imkonini beradigan material dizayni yondashuvidir. Ushbu tadqiqot pentatsen molekulalarining para-terphenyl (PTP), perdeuterated para-terphenyl (PTP-d₁₄), naphthalene (NAP) va picene (PIC) kristallaridagi xona haroratidagi triplet-spin dinamikasini transient electron paramagnetic resonance (trEPR), optically detected magnetic resonance (ODMR), fluorescence spectroscopy, Raman spectroscopy, density-functional-theory bilan qoʻllab-quvvatlangan tebranish tahlili va haqiqiy maser tajribalari yordamida taqqoslaydi.

Asosiy tadqiqot savoli pentatsenning kimyoviy tuzilishini butunlay oʻzgartirmasdan, faqat uni oʻrab turgan kristall panjara yoki izotop tarkibini oʻzgartirib, maser uchun zarur boʻlgan uch xususiyat — kuchli triplet spin polarization, sekin spin-lattice relaxation va tor mikrotoʻlqin resonance line width — oʻrtasida yaxshiroq muvozanat yaratish mumkinmi, degan masaladir.

Tadqiqotda taqqoslangan asosiy tizimlar:

• Pc:PTP: pentatsen + para-terphenyl,
• Pc-d₁₄:PTP-d₁₄: perdeuterated pentatsen + perdeuterated para-terphenyl,
• Pc:NAP: pentatsen + naphthalene,
• Pc:PIC: pentatsen + picene.

Natijalar mezbon kristallning mexanik qattiqligi va tebranish spektri pentatsenning triplet sublevel populations, triplet depopulation rates va spin-lattice relaxation rates ko‘rsatkichlariga kuchli taʼsir qilishini ko‘rsatadi. Qattiq fused-ring mezbonlardan picene ayniqsa \(|T_z\rangle\) holatini o‘z ichiga olgan spin-lattice relaxation jarayonlarini sezilarli darajada sekinlashtira oladi. Biroq picene muhiti pentatsen ustida strain hosil qilib, taxminan 7 MHz kenglikdagi \(|T_x\rangle\leftrightarrow|T_z\rangle\) resonance line width va pastroq spin polarization yuzaga keltiradi.

Perdeuterated Pc-d₁₄:PTP-d₁₄ tizimi boshqa afzallikni ko‘rsatadi. Vodorodning og‘irroq izotopi deuterium bilan almashtirilishi C–D tebranishlarining C–H tebranishlariga nisbatan pastroq chastotada sodir bo‘lishiga, vibrationally mediated triplet depopulation sekinlashishiga va proton manbali hyperfine broadening kamayishiga hissa qo‘shadi. Ushbu tizimda \(|T_x\rangle\leftrightarrow|T_z\rangle\) CW-ODMR line width taxminan 1,4 MHz deb o‘lchangan va pulsed maser tajribasida atigi 0,9 mJ optical pulse energy bilan masing chegarasiga erishilgan. Xuddi shu tajriba sharoitida Pc:PTP uchun chegara 2,4 mJ, Pc:NAP uchun 4 mJ bo‘lgan.

Biroq tadqiqot continuous-wave maser eksperimental ravishda ishga tushirilganini ko‘rsatmaydi. Haqiqiy qurilma tajribalari pulsed masing bilan bog‘liq. Continuous-wave (CW) ishlash uchun triplet population kinetics, tajribaviy spin-relaxation parametrlari va maser cooperativity yordamida simulyatsiya qilingan. Ushbu simulyatsiyalarda Pc-d₁₄:PTP-d₁₄ to‘rt nomzod orasida eng yuqori continuous-operation cooperativity qiymatini saqlaydigan tizim sifatida ajralib turadi.

Picene muhim fizik farqni ko‘rsatadi: spin-lattice relaxation ni sekinlashtirish uchun triplet lifetime albatta uzayishi shart emas. Pc:PIC da \(|T_z\rangle\) bilan bog‘liq spin-lattice relaxation kuchli bostirilgan bo‘lsa-da, \(k_x\) va \(k_y\) triplet depopulation rates Pc:PTP ga yaqin qoladi. Bu mos kristall muhiti ayrim istalmagan spin-relaxation yo‘llarini tanlab kamaytirishi mumkinligini ko‘rsatadi. Ammo picene ning strain-induced 7 MHz line broadening i native resonator quality factor sharoitida masing ni to‘sib qo‘ygan.

Tadqiqotning umumiy xulosasi bitta parametrni maksimal qilishning o‘zi yetarli emasligidir. Ideal xona-haroratli molekulyar maser materiali bir vaqtning o‘zida kuchli population inversion, mos triplet recycling, past spin-lattice relaxation, tor resonance line width va yetarli spin coherence ni taʼminlashi kerak. Mualliflar taqqoslagan tizimlar orasida ushbu muvozanatni eng yaxshi taʼminlaydigan nomzod perdeuterated Pc-d₁₄:PTP-d₁₄ dir.

Ushbu tadqiqotdagi “kvant” nimani anglatadi?

Ushbu tadqiqotdagi kvant xatti-harakati molekulalardagi juftlashmagan elektronlarning diskret spin energiya sathlari, bu sathlar orasidagi koherent mikrotoʻlqin oʻtishlari, optik ravishda yaratilgan spin polarization va population inversion bilan bogʻliq; tadqiqot kvant kompyuter algoritmlari yoki qubit darvoza sxemalari haqida emas.

Elektron spinini klassik tarzda aylanayotgan kichik shar sifatida tushunish kerak emas. Spin elektronning kvant-mexanik ichki burchak momenti bilan bog‘liq fundamental xususiyatdir. Molekulada bir nechta juftlashmagan elektron bo‘lsa, umumiy spin holati muayyan kvant sathlariga ajralishi mumkin.

Pentatsen optik ravishda qoʻzgʻatilganda avval singlet excited state ga oʻtadi. Keyin spin-selektiv intersystem crossing (ISC) orqali triplet manifoldiga oʻtish sodir boʻlishi mumkin.

Tadqiqotdagi asosiy fotofizik zanjir:

\[ |S_0\rangle \xrightarrow{\text{optik uyarım}} |S_1\rangle \xrightarrow{\mathrm{ISC}} |T\rangle \rightarrow |T_x\rangle,\ |T_y\rangle,\ |T_z\rangle \]

koʻrinishida konseptuallashtirilishi mumkin.

\(|S_0\rangle\) elektron singlet ground state, \(|S_1\rangle\) optik ravishda erishiladigan excited singlet state, \(|T_x\rangle\), \(|T_y\rangle\), \(|T_z\rangle\) esa photoexcited triplet manifoldining zero-field-split spin quyi sathlaridir.

Maser nima?

MASER, Microwave Amplification by Stimulated Emission of Radiation iborasining qisqartmasidir. Fizik prinsipi lazerga oʻxshaydi; biroq elektromagnit chiqish koʻrinadigan yorugʻlik emas, mikrotoʻlqin sohasidadir.

Maser ishlashi uchun ikki energiya sathi orasida population inversion talab qilinadi. Bu yuqori energiyali spin sathida quyi sathga nisbatan yetarlicha ko‘p population bo‘lishini anglatadi.

Ushbu tadqiqotda asosiy maser oʻtishi:

\[ |T_x\rangle\leftrightarrow|T_z\rangle \]

oʻtishi boʻlib, chastotasi ishlatilgan host ga qarab taxminan 1,44–1,45 GHz atrofidadir.

Mikrotoʻlqin fotoni ushbu ikki sath orasidagi energiya farqi bilan rezonansga kelganda stimulated emission ishga tushishi mumkin. Yetarli population inversion va yetarlicha past cavity loss bo‘lsa, mikrotoʻlqin maydoni kuchayadi.

Nega triplet holatlaridan foydalaniladi?

Singlet excited states ko‘p molekulalarda nanosekund miqyosida tez so‘nishi mumkin. Pentatsen triplet states esa spin selection rules sabab uzoqroq yashashi va population inversion ni mikrotoʻlqin stimulated emission uchun yetarlicha uzoq saqlashga imkon berishi mumkin.

Triplet state ning uchta spin quyi sathga ajralishi elektron-elektron dipolar interaction sababli yuzaga keladigan zero-field splitting (ZFS) natijasidir.

Zero-field splitting D va E parametrlari nimani anglatadi?

Zero-field splitting parametrlari \(D\) va \(E\), tashqi magnit maydon bo‘lmasa ham triplet elektronlarining dipolyar o‘zaro taʼsiri tufayli \(S=1\) spin manifoldining energiya sathlari bir-biridan ajralishini tavsiflaydi.

Supporting Information da ishlatilgan triplet spin Hamiltoniani:

\[ H= D\left(S_z^2-\frac{1}{3}S^2\right) + E\left(S_x^2-S_y^2\right) + g_e\mu_B\mathbf{B}_0\cdot\mathbf{S}. \]

Bu yerda:

• \(H\): spin Hamiltoniani,
• \(D\): axial zero-field splitting parametri,
• \(E\): rhombic zero-field splitting parametri,
• \(S_x,S_y,S_z\): umumiy elektron spin operatorining komponentlari,
• \(S=1\): triplet umumiy spin kvant soni,
• \(g_e\approx2.0023\): elektron g faktori,
• \(\mu_B\): Bohr magnetoni,
• \(\mathbf{B}_0\): qoʻllangan external magnetic field.

Birinchi ikki had external field bo‘lmaganda elektron–elektron dipolar coupling hosil qiladigan splitting ni; oxirgi had esa external field ostidagi Zeeman interaction ni ifodalaydi.

Asosiy trEPR fit natijalari:

D va E ning barcha host larda bir-biriga yaqin qolishi asosiy pentatsen triplet electronic structure saqlanishini ko‘rsatadi. Biroq population ratios ning sezilarli o‘zgarishi host intersystem crossing va vibrational coupling yo‘llariga jiddiy taʼsir qilishini ko‘rsatadi.

Mezbon kristall pentatsenning spin holatini nega o‘zgartira oladi?

Mezbon kristall pentatsenning elektron tuzilishini butunlay o‘zgartirmasdan, molekula atrofidagi mexanik siqilishni, intermolecular packing ni, out-of-plane tebranishlarni, spin–phonon coupling ni va nuclear-spin environment ni o‘zgartirish orqali ISC, triplet depopulation va spin-lattice relaxation tezliklarini o‘zgartira oladi.

Out-of-plane “butterfly” tebranishlari

Pentatsenning spin-selective ISC si faqat elektron energy levels ga emas, molecular vibrations ga ham bog‘liq. Ayniqsa molekula tekisligidan tashqariga chiqadigan asymmetric out-of-plane (OOP) harakatlar pentatsenning π-orbital tizimidagi local symmetry ni vaqtincha buzishi mumkin.

Ushbu symmetry breaking odatda kuchsiz bo‘lgan orbital coupling yo‘llarini ochib, singlet va triplet states orasidagi intersystem crossing ni osonlashtirishi mumkin.

Manba ushbu tebranishlarni “butterfly modes” deb muhokama qiladi.

Nega para-terphenyl afzallik berishi mumkin?

Para-terphenyl rotationally compliant mezbondir. Fenil halqalari orasidagi bog‘lar pentatsenning OOP distortions iga maʼlum darajada moslasha oladi. Bu moslashuvchanlik kuchli spin-selective ISC va aniq \(|T_x\rangle\) population hosil bo‘lishi jihatidan afzallik beradi.

Naphthalene va picene nega farq qiladi?

NAP va PIC fused-ring tuzilmalar bo‘lib, qattiqroq local environments taʼminlaydi. Bu qattiqlik ayrim lattice vibrations amplitudasini kamaytirib, spin-lattice relaxation ni bostirishi mumkin.

Ammo bu afzallikning narxi bor:

• ISC-promoting distortions ning cheklanishi,
• triplet spin polarization ning kamayishi,
• host–guest strain ning ortishi,
• ayniqsa PIC da resonance line broadening.

Intermolecular spacing hisoblash

Supporting Information da host lattice confinement ni taqqoslash uchun taxminiy intermolecular length scale ishlatilgan:

\[ d_{\mathrm{host}} \approx \left( \frac{M}{\rho N_A} \right)^{1/3}. \]

Bu yerda:

• \(M\): molar mass,
• \(\rho\): host material density,
• \(N_A\): Avogadro doimiysi,
• \(d_{\mathrm{host}}\): har bir molekula uchun volume dan kelib chiqadigan taxminiy o‘rtacha intermolecular spacing.

Hisoblangan qiymatlar:

Bu sonlar to‘g‘ridan-to‘g‘ri “host rigidity” o‘lchovi emasligini taʼkidlash muhim. Tenglama packing density uchun soddalashtirilgan spatial-confinement metric beradi. NAP ning kichikroq qiymati pentatsen uchun torroq sterik muhitga mos keladi; mexanik qattiqlik esa molecular connectivity va lattice dynamics kabi boshqa xususiyatlarga ham bog‘liq.

Deuteratsiya nega spin dinamikasini o‘zgartiradi?

Deuteratsiya molekuladagi vodorod atomlarini og‘irroq vodorod izotopi deuterium bilan almashtirishdir; og‘irroq C–D oscillator lari C–H bog‘lariga qaraganda pastroq tebranish chastotalariga ega va proton nuclear spins kamaygani sabab vibrational relaxation hamda hyperfine broadening o‘zgarishi mumkin.

Pc-d₁₄:PTP-d₁₄ tizimida ham mehmon pentatsen, ham host para-terphenyl perdeuterated shakldadir.

Manba deuteration ning ikki muhim taʼsirini ajratadi:

1. Triplet state dan singlet ground state ga vibrationally mediated non-radiative depopulation sekinlashadi.
2. Spin-transition line width torayadi.

Biroq deuteration barcha coherence o‘lchovlarini bir xil darajada yaxshilamagan. Zero-field optically detected Hahn-echo o‘lchovlarida:

Pc-d₁₄:PTP-d₁₄ ning Hahn-echo \(T_2\) qiymati protiated Pc:PTP dan faqat cheklangan darajada farq qiladi. Mualliflar bu barcha namunalarda umumiy bo‘lgan boshqa decoherence mechanism ustun bo‘lishi mumkinligini va concentration-dependent electron–electron dipole interactions ehtimoliy nomzod ekanini taʼkidlaydi.

Shu sabab “deuteratsiya spin coherence ni har qanday sharoitda bir necha baravar oshirdi” degan xulosaga kelib bo‘lmaydi.

Fluorescence lifetime bilan intersystem crossing orasidagi bog‘lanish qanday aniqlanadi?

Mezbonlar qutbsiz ekani va singlet radiative transition dipole moment katta darajada o‘zgarmasligi kutilishi farazi ostida fluorescence lifetime dagi farqlar intersystem crossing va non-radiative internal conversion tezliklaridagi o‘zgarishlar haqida bilvosita maʼlumot berishi mumkin; biroq fluorescence lifetime o‘zi ISC tezligining bevosita o‘lchovi emas.

Manbada:

\[ \frac{1}{\tau_f} = k_r+k_{\mathrm{ISC}}+k_{\mathrm{IC}} \]

munosabatidan foydalaniladi.

Bu yerda:

• \(\tau_f\): fluorescence lifetime,
• \(k_r\): radiative fluorescence rate,
• \(k_{\mathrm{ISC}}\): intersystem-crossing rate,
• \(k_{\mathrm{IC}}\): non-radiative internal-conversion rate.

Supporting Information da TCSPC fluorescence decay egri chiziqlari instrument-response function bilan convolution ni o‘z ichiga olgan monoexponential modelga fit qilingan:

\[ I_{\mathrm{fit}}(t) = I_0 \left[ \mathrm{IRF}(t) \otimes \exp\left(-\frac{t}{\tau}\right) \right] +C. \]

Bu yerda \(I_0\) pre-exponential amplitude, IRF o‘lchangan instrument response function, \(\tau\) fluorescence lifetime va \(C\) background offset.

Pc:NAP ning uzoqroq fluorescence lifetime i reduced ISC bilan mos keladi va manba buni ilgari xabar qilingan taxminan %40 ISC yield bilan bog‘laydi. Pc:PTP uchun ilgari xabar qilingan ISC yield taxminan %62,5 dir.

Pc:PIC eng qisqa fluorescence lifetime ga ega. Mualliflar buni picene muhitida tezroq ISC ehtimoli bilan muhokama qiladi; biroq tadqiqot pentatsenning PIC ichidagi ISC yield ini bevosita yangi foiz sifatida o‘lchamaydi.

Optik absorption o‘zgarishlari

Pc:PTP referensiga nisbatan lowest-energy singlet absorption:

• Pc:NAP uchun taxminan 598 nm ga red-shift,
• Pc:PIC uchun taxminan 592 nm ga red-shift,
• Pc-d₁₄:PTP-d₁₄ uchun taxminan 587 nm ga blue-shift

ko‘rsatadi.

Mualliflar deuterated tizimdagi blue shift ni C–D stretching modes bilan, NAP/PIC red shift larini esa host bilan ortgan π–π interaction natijasida pentatsen LUMO sathining barqarorlashishi bilan bog‘laydi. Bular manba mualliflarining fizik talqinlaridir.

Raman va DFT tahlillari nimani tasdiqlaydi?

Raman/DFT bo‘limi host packing va isotope substitution pentatsen bilan bog‘liq out-of-plane vibrational landscape ni o‘zgartira olishini qo‘llab-quvvatlaydi; biroq pentatsen konsentratsiyasi past bo‘lgani sabab eksperimental Raman spektrida pentatsen tebranishlarini bevosita va aniq ajratib olish mumkin bo‘lmagan.

DFT hisoblari Gaussian yordamida:

• B3LYP exchange-correlation functional,
• 6-31G(d,p) basis set,
• geometry optimization,
• vibrational-frequency calculation

bajarilgan.

Optimization dan so‘ng frequency calculations orqali tuzilmalarning true minimum ekani tekshirilgan.

Supporting Information da host molecules uchun tanlangan Raman-active modes:

Pc:NAP past chastotali OOP modes bo‘yicha gas-phase pentacene referensidan eng katta o‘zgarishni ko‘rsatadi. Bu NAP torroq spatial confinement taʼminlashi bilan mos keladi.

Biroq asosiy matnda mualliflar pentatsenning host ichidagi muayyan vibrational modes ini Raman tajribasidan aniq ajrata olmaganlarini ochiq aytadi. Past dopant concentration bu ajratishni qiyinlashtiradi.

EPR va ODMR o‘rtasidagi farq nima?

EPR elektron spin resonance ni to‘g‘ridan-to‘g‘ri mikroto‘lqin absorption/emission orqali kuzatsa, ODMR mikroto‘lqin yordamida spin population o‘zgartirilgandan keyin uning photoluminescence ga taʼsirini optik tarzda aniqlaydi; tadqiqotda ikki usul bir-birini to‘ldirib, spin Hamiltoniani, population, relaxation va coherence haqida maʼlumot beradi.

Transient EPR

Transient X-band EPR:

• xona haroratida,
• Bruker ELEXSYS E500T tizimi,
• ER4118X-MD-5W resonator,
• 20 Hz Q-switched Nd:YAG pumped OPO,
• taxminan 5 mJ optical pulse energy,
• 5–7 ns pulse duration

yordamida bajarilgan.

Pc:PTP, Pc:NAP va Pc-d₁₄:PTP-d₁₄ uchun 590 nm; Pc:PIC uchun 530 nm excitation ishlatilgan.

Powder EPR spectra EasySpin 6.0.10 yordamida spin Hamiltonian ga fit qilingan.

ODMR

ODMR measurements xona haroratida va zero applied magnetic field ostida o‘tkazilgan.

520 nm laser excitation ishlatilgan. Pulsed spin-dynamics tajribalarida jami 22 ta alohida relaxation trace bir vaqtning o‘zida coupled rate-equation modeliga fit qilingan.

O‘lchov protokolida:

• 5 µs optical initialization pulse,
• 0,5 µs readout pulse,
• Sequence B uchun 30 µs readout delay,
• 600 µs repetition time

ishlatilgan.

600 µs repetition time o‘lchovlar orasida population ning singlet ground state ga to‘liq qaytishi uchun vaqt berish maqsadida tanlangan.

Zero-field ODMR transition frequencies

Rabi tebranishi nimani ko‘rsatadi?

Rabi tebranishi rezonansli mikroto‘lqin maydoni spin population ni ikki kvant sathi o‘rtasida koherent tarzda aylantira olishini ko‘rsatadigan time-domain oscillation dir; tebranish chastotasi microwave drive strength bilan, so‘nish tezligi esa decoherence jarayonlari bilan bog‘liq.

Transient-EPR Rabi traces manbada zero-order Bessel function yordamida fit qilingan:

\[ I(t) = A\,J_0\!\left[\Omega(t-t_0)\right] \exp[-\Gamma(t-t_0)] + C. \]

Bu yerda:

• \(I(t)\): measured time-domain EPR signal,
• \(A\): initial spin polarization ga bog‘liq oscillation amplitude,
• \(J_0\): zero-order Bessel function,
• \(\Omega\): Rabi angular frequency,
• \(t_0\): timing offset,
• \(\Gamma\): damping rate,
• \(C\): constant background.

Rabi frequency ning microwave power kvadrat ildizi bilan chiziqli ortishi coherent microwave driving bilan mos keladi.

Manbada high-field absorption feature uchun chiqarilgan \(T_{2,\mathrm{Rabi}}\) qiymatlari low-field emission feature qiymatlaridan taxminan ikki baravar uzun bo‘lishi low-field sohada hyperfine-mediated electron–nuclear spin mixing kuchliroq ekani bilan tushuntiriladi.

Ushbu \(T_{2,\mathrm{Rabi}}\) qiymatlarini zero-field Hahn-echo \(T_2\) qiymatlari bilan aynan bir xil kattalik deb baholash to‘g‘ri emas. Turli pulse sequence, field regime va extraction usuli ishlatilgan.

Spin-panjara relaksatsiyasi va triplet umri bir xil narsami?

Yo‘q; spin-panjara relaksatsiyasi \(|T_x\rangle\), \(|T_y\rangle\) va \(|T_z\rangle\) triplet quyi sathlari orasidagi population transferini tavsiflasa, \(k_x\), \(k_y\) va \(k_z\) triplet population ning singlet ground state ga qaytishini tavsiflaydi.

Bu farq tadqiqotning asosiy natijalaridan biridir.

Spin-lattice relaxation rates:

• \(\omega_{xy}\),
• \(\omega_{yz}\),
• \(\omega_{xz}\)

triplet sublevels orasidagi population exchange ni o‘lchaydi.

Triplet depopulation rates:

• \(k_x\),
• \(k_y\),
• \(k_z\)

esa tegishli triplet state dan singlet ground state ga decay ni o‘lchaydi.

Barcha host larda:

\[ \omega_{yz}>\omega_{xz}>\omega_{xy} \]

ketma-ketligi saqlanadi.

Eng sezilarli o‘zgarish Pc:PIC da \(|T_z\rangle\) bilan bog‘liq relaxation rates da ko‘rinadi:

\[ \omega_{yz}: 2.19\rightarrow0.8\times10^4\ \mathrm{s^{-1}} \]

va:

\[ \omega_{xz}:1.17\rightarrow0.37\times10^4\ \mathrm{s^{-1}} \]

Pc:PTP ga nisbatan jiddiy kamayadi.

Bunga qarshi ravishda Pc:PIC dagi:

\[ k_x=2.37\times10^4\ \mathrm{s^{-1}} \]

va:

\[ k_y=1.26\times10^4\ \mathrm{s^{-1}} \]

Pc:PTP ga juda yaqin.

Bu natija rigid host spin-sublevel redistribution ni sekinlashtirgan holda triplet state ning singlet ground state ga qaytishini xuddi shu darajada sekinlashtirishi shart emasligini ko‘rsatadi.

Resonance line width nega maser uchun muhim?

Resonance line width spin ensemble rezonans chastotalari qanchalik keng taqsimotga yoyilishini belgilaydi; line width kattalashgani sari bir xil cavity mode bilan koherent o‘zaro taʼsir qila oladigan spinlarning samarali ulushi kamayadi va population inversion ni microwave gain ga aylantirish qiyinlashadi.

0,01% Pc-d₁₄:PTP-d₁₄ namunasida 0,55 MHz line width kuzatilishi concentration-dependent electron–electron dipolar broadening ham muhimligini qo‘llab-quvvatlaydi.

Pc:PIC Hahn-echo da eng uzun \(T_2=1.51\) µs qiymatiga ega bo‘lsa-da, 7 MHz juda keng static line width ko‘rsatadi. Mualliflar bu farqni static strain broadening va dynamic decoherence o‘rtasidagi farq bilan izohlaydi.

Demak tor line width va uzun Hahn-echo \(T_2\) bir xil narsani o‘lchamaydi.

Tadqiqot Usuli va Natijalari

To‘rtta host–guest tizimi qanday tayyorlangan?

Pentatsen yoki perdeuterated pentatsen past molyar nisbatlarda tozalangan aromatic host crystals ichiga qo‘shilgan va single crystals Bridgman usuli bilan o‘stirilgan; shu tariqa pentacene molecules host lattice ichidagi muayyan substitution sites ga joylashgan holda, bir-biri bilan ortiqcha aggregation hosil qilmaydigan darajada suyultirilgan.

Ishlatilgan materiallar

PTP, NAP va PTP-d₁₄ crystal growth dan oldin kamida 20 marta zone-refined qilingan. Pentacene va picene high vacuum ostida sublimed qilingan. Pentacene-d₁₄ esa sotib olingan holicha ishlatilgan.

Doping nisbatlari

Pc:PTP, Pc-d₁₄:PTP-d₁₄ va Pc:PIC uchun nominal pentacene concentration:

\[ 0.1\ \mathrm{mol\%} \]

sifatida tanlangan.

Pc:NAP uchun trEPR experiment dastlab aggregation xavfini kamaytirish maqsadida:

\[ 0.01\ \mathrm{mol\%} \]

ishlatilgan.

Maser va ODMR measurements uchun Pc:NAP loading:

\[ 0.04\ \mathrm{mol\%} \]

darajasiga oshirilgan.

Manba ushbu concentrations o‘xshash spin-guest densities hosil qilishini qayd etadi:

• 0,04% Pc:NAP: taxminan \(2.1\times10^{24}\ \mathrm{m^{-3}}\),
• 0,1% Pc:PTP: taxminan \(3.3\times10^{24}\ \mathrm{m^{-3}}\),
• 0,1% Pc:PIC: taxminan \(2.9\times10^{24}\ \mathrm{m^{-3}}\).

Bu zichliklar diamond NV maserlarida ishlatiladigan ppm-scale defect concentrations dan ancha yuqori; biroq yuqoriroq spin concentration electron–electron dipolar broadening xavfini ham oshirishi mumkin.

Bridgman crystal growth

Guest va host powders birga maydalangan, borosilicate naychalarga solingan va taxminan 900 mbar argon ostida sealed qilingan.

PIC uchun pastroq growth rate yuqori temperature gradient sabab thermal stress ni kamaytirish uchun qo‘llangan.

Pc:PIC crystal preparation vaqtida qora material ajralishi kuzatilgan va bu picene ning yuqori melting point i tufayli pentacene degradation bilan bog‘liq bo‘lishi mumkinligi qayd etilgan. Keyingi tajribalarda eng yaxshi ko‘ringan crystal segments tanlangan.

Optik xarakterizatsiya

UV–vis absorption Agilent Cary 5000 UV–Vis–NIR spectrophotometer yordamida o‘lchangan.

TCSPC uchun:

• 530 nm NanoLED,
• <200 ps optical pulses,
• 1 mW cm⁻² excitation density,
• 1 MHz repetition frequency

ishlatilgan.

Raman spectroscopy Renishaw inVia system va 785 nm diode laser yordamida bajarilgan.

trEPR

X-band transient EPR xona haroratida Bruker ELEXSYS E500T bilan bajarilgan.

Powder spectra EasySpin 6.0.10 toolbox yordamida spin Hamiltonian modeliga fit qilingan.

ODMR

Zero-field ODMR da 520 nm excitation, photoluminescence detection, microwave pulse sequences va photon-counting ishlatilgan.

Pulsed relaxation analysis jami 22 ta alohida time traces ni umumiy rate-equation modeliga simultaneous fit qiladi.

Triplet population kinetikasi qanday modellashtiriladi?

Continuous-operation baholashida singlet ground state, excited singlet state va uch triplet sublevel uchun beshta bog‘langan rate equation yechilib, optical pumping, ISC, triplet depopulation va spin-lattice relaxation population inversion ni vaqt davomida qanday o‘zgartirishi hisoblangan.

Supporting Information dagi tenglamalar tizimi:

\[ \frac{dS_0}{dt} = -k_{01}S_0 +k_{10}S_1 +k_xT_x +k_yT_y +k_zT_z \]

\[ \frac{dS_1}{dt} = k_{01}S_0 - (k_{10}+k_{\mathrm{ISC}})S_1 \]

\[ \frac{dT_x}{dt} = k_{\mathrm{ISC}}P_xS_1 - (k_x+\omega_{xy}+\omega_{xz})T_x + \omega_{yx}T_y + \omega_{zx}T_z \]

\[ \frac{dT_y}{dt} = k_{\mathrm{ISC}}P_yS_1 - (k_y+\omega_{yx}+\omega_{yz})T_y + \omega_{xy}T_x + \omega_{zy}T_z \]

\[ \frac{dT_z}{dt} = k_{\mathrm{ISC}}P_zS_1 - (k_z+\omega_{zx}+\omega_{zy})T_z + \omega_{xz}T_x + \omega_{yz}T_y. \]

Tenglamalarda:

• \(S_0\): singlet ground-state population,
• \(S_1\): optically excited singlet population,
• \(T_x,T_y,T_z\): triplet sublevel populations,
• \(k_{01}\): optical pumping rate,
• \(k_{10}\): singlet de-excitation rate,
• \(k_{\mathrm{ISC}}\): intersystem-crossing rate,
• \(P_x,P_y,P_z\): ISC dan keyin tegishli triplet sublevel ga branching fractions,
• \(k_x,k_y,k_z\): triplet depopulation rates,
• \(\omega_{ij}\): spin-lattice population-transfer rates.

Continuous-light simulation da:

\[ k_{01}=1.1\times10^8\ \mathrm{s^{-1}} \]

pump rate ishlatilgan.

Bu yerda muhim model cheklovi mavjud. Pc:NAP uchun \(k_{\mathrm{ISC}}\) avvalgi adabiyotdan baholangan. Pc:PIC uchun \(k_{\mathrm{ISC}}\) Pc:PTP bilan bir xil deb qabul qilingan. Shu sabab Figure 7 dagi continuous-operation curves butunlay mustaqil yangi o‘lchovlar emas; measured rates va literature/assumption parameters birgalikda ishlatilgan.

ODMR orqali chiqarilgan population taqsimotlari

Bu yerdagi \(P_x,P_y,P_z\) qiymatlari o‘zaro normallashtirilgan:

\[ P_x+P_y+P_z=1. \]

Bu ODMR-derived population qiymatlari asosiy matndagi trEPR-derived Table I population ratios bilan aynan bir xil emas. Ikki usulning excitation, field condition va fitting yondashuvi farq qiladi; qiymatlar bir-birining nusxasi sifatida ishlatilmasligi kerak.

Maser cooperativity nima?

Maser cooperativity \(\eta_{\mathrm{maser}}\) spin ensemble va microwave cavity orasidagi collective gain cavity losses ga nisbatan qanchalik kuchli ekanini ifodalovchi o‘lchovsiz ko‘rsatkichdir; continuous-wave masing uchun tadqiqotda ishlatilgan mezon \(\eta_{\mathrm{maser}}>1\) dir.

Manbada:

\[ \eta_{\mathrm{maser}} = \left( \frac{\mu_0g^2\mu_B^2}{h} \right) \eta_{\mathrm{mag}} \frac{Q\,\Delta N} {V_{\mathrm{mag}}\Delta f} \]

ko‘rinishida beriladi.

Bu yerda:

• \(\mu_0\): vacuum permeability,
• \(g\): elektron spin g-factor,
• \(\mu_B\): Bohr magnetoni,
• \(h\): Planck doimiysi,
• \(\eta_{\mathrm{mag}}\): magnetic filling factor,
• \(Q\): resonator quality factor,
• \(\Delta N\): \(|T_x\rangle\) va \(|T_z\rangle\) orasidagi population inversion,
• \(V_{\mathrm{mag}}\): effective magnetic mode volume,
• \(\Delta f\): maser transition effective line width.

Tenglama juda aniq dizayn qoidasini beradi:

• \(Q\) oshsa, cooperativity oshadi.
• Population inversion \(\Delta N\) oshsa, cooperativity oshadi.
• Line width \(\Delta f\) kattalashsa, cooperativity kamayadi.
• Effective mode volume kattalashgani sari bir xil spin soni uchun coupling zaiflashishi mumkin.

Shuning uchun faqat uzun triplet lifetime yetarli emas. Juda keng line width yaxshi population inversion ni ham foydasiz holga keltirishi mumkin.

Continuous-operation simulation parametrlari

Ushbu simulation Pc-d₁₄:PTP-d₁₄ tizimi to‘rt material orasida continuous operation sharoitida eng yuqori \(\eta_{\mathrm{maser}}\) darajasini saqlashini ko‘rsatadi.

Bu natija bevosita CW maser tajribasining natijasi emas.

Haqiqiy maser tajribasida qaysi tizim yaxshiroq ishladi?

High-Q strontium-titanate resonator bilan o‘tkazilgan pulsed maser tajribasida Pc-d₁₄:PTP-d₁₄ eng past optical threshold va eng yuqori microwave output ni berdi; Pc:NAP yuqoriroq threshold va zaif output ko‘rsatgan bo‘lsa, Pc:PIC native resonator Q ostida umuman maser signali hosil qilmadi.

Maser setup uchun measured quality factor taxminan:

\[ Q\sim3000 \]

va coupling strength taxminan:

\[ -0.1\ \mathrm{dB} \]

sifatida berilgan.

Pc-d₁₄:PTP-d₁₄ nega past threshold berdi?

Manba talqiniga ko‘ra uch afzallik birgalikda ishlaydi:

• kuchli triplet spin polarization,
• tor, taxminan 1,4 MHz \(|T_x\rangle\leftrightarrow|T_z\rangle\) line width,
• deuteration sabab kamaygan vibrational triplet depopulation.

Bu kombinatsiya cavity ichidagi kattaroq spin fraction ning ayni microwave mode bilan rezonansli o‘zaro taʼsirga kirishiga va pastroq optical pumping bilan population inversion ning masing threshold dan oshishiga imkon beradi.

Pc:NAP nega zaif qoldi?

Pc:NAP:

• uzoqroq fluorescence lifetime,
• reduced ISC,
• pastroq triplet polarization,
• sekin triplet depopulation

ko‘rsatadi.

Maser uchun faqat triplet ning uzoq yashashi yetarli emas. Kuchli initial population inversion hosil qilinmasa, cavity gain yetarli bo‘lmasligi mumkin. Pc:NAP ning 4 mJ threshold va zaifroq microwave output ko‘rsatishi shu muvozanatni aks ettiradi.

Pc:PIC nega native resonator bilan ishlamadi?

Pc:PIC ning afzalligi past spin-lattice relaxation; biroq 7 MHz line width va past initial \(|T_x\rangle\) polarization bu afzallikni maser gain ga aylantirishni qiyinlashtiradi.

Native cavity da masing kuzatilmagan.

Mualliflar keyinroq cavity loss ni elektron feedback bilan sunʼiy ravishda kamaytiradigan Q-boosted qurilma yaratgan.

Effective Q taxminan:

\[ Q\sim150000 \]

darajasiga ko‘tarilganda Pc:PIC dan taxminan:

\[ 50\ \mu\mathrm{s} \]

davom etadigan maser pulse kuzatilgan.

Yaqindagi permanent magnet bilan resonance detune qilinganda signal yo‘qolgan va signalning pentacene triplet-state resonance bilan bog‘liqligi tekshirilgan.

Bu tajriba ham continuous-wave operation emas.

STO maser resonator

Single crystals high-Q strontium titanate (STO) resonator ichiga joylashtirilgan. Axisymmetric TE₀₁δ microwave mode ning AC magnetic field i pentacene:

\[ |T_x\rangle\leftrightarrow|T_z\rangle \]

transition ini boshqaradi.

Host–guest crystals monoclinic \(P2_1/a\) lattice da pentacene molecules muayyan orientations da substitutional sites ni egallashi sabab kamida bitta molecular orientation cavity magnetic field bilan mos coupling taʼminlashi mumkin.

Tadqiqot qo‘llab-quvvatlaydigan xulosalar

• Host crystal tanlovi pentacene triplet spin dynamics ni xona haroratida o‘lchash mumkin bo‘lgan darajada o‘zgartiradi.
• Host rigidity va vibrational coupling spin-lattice relaxation hamda triplet depopulation rates ni sozlash uchun ishlatilishi mumkin.
• Pc:PIC \(|T_z\rangle\) ni o‘z ichiga olgan spin-lattice relaxation pathways ni Pc:PTP ga nisbatan kuchli kamaytiradi.
• Pc:PIC dagi bu afzallik triplet lifetime ning umumiy ravishda uzayishini talab qilmaydi.
• Picene qattiqligi bir vaqtning o‘zida strain-induced line broadening va past triplet polarization kamchiligini yuzaga keltiradi.
• Deuteration triplet depopulation rates ni kamaytiradi va \(|T_x\rangle\leftrightarrow|T_z\rangle\) resonance line width ni toraytiradi.
• Pc-d₁₄:PTP-d₁₄ pulsed maser tajribasida 0,9 mJ bilan eng past optical threshold ni beradi.
• Pc:NAP pulsed maser threshold 4 mJ bilan yuqoriroq.
• Pc:PIC native-Q resonator ostida maser hosil qilmaydi; Q-boost bilan qisqa maser pulse olish mumkin.
• Continuous-operation modeling to‘rt nomzod ichida Pc-d₁₄:PTP-d₁₄ tizimini eng mos CW maser nomzodi sifatida ko‘rsatadi.

Tadqiqot qo‘llab-quvvatlamaydigan xulosalar

• Tadqiqot eksperimental continuous-wave organik maser amalga oshirmagan.
• Pc-d₁₄:PTP-d₁₄ ning haqiqiy qurilmada cheksiz muddat CW ishlashi isbotlanmagan.
• Pc:PIC “yomon kvant materiali” emas; aksincha spin-lattice relaxation jihatidan afzal, ammo maser line width jihatidan noqulay trade-off ko‘rsatadi.
• Deuteration barcha spin-coherence metrikalarini katta darajada uzaytirmagan.
• Fluorescence lifetime bevosita ISC yield o‘lchovi emas.
• Raman experiment pentatsenning barcha host-specific OOP vibrational modes ini bevosita ajrata olmagan.
• Continuous-operation population simulations faqat o‘lchangan parametrlarga asoslanmaydi; ayrim ISC rates adabiyotdan olingan yoki faraz qilingan.
• Q-boosted Pc:PIC pulse tabiiy cavity sharoitida yuqori samarali CW maser dalili emas.
• Ushbu tadqiqot molekulyar quantum computing gate fidelity yoki qubit algorithm performance ni o‘lchamaydi.

Tadqiqotning dizayn bo‘yicha eng muhim xabari

Eng yaxshi molekulyar spin materialini faqat eng uzun \(T_2\), eng uzun triplet lifetime yoki eng past spin-lattice relaxation qiymatini tanlash orqali topib bo‘lmaydi.

Maser nuqtai nazaridan bir vaqtning o‘zida:

• yuqori triplet yield,
• kuchli \(|T_x\rangle\) population,
• yetarlicha tez unwanted-state recycling,
• sekin zararli spin-lattice redistribution,
• tor resonance line width,
• mos spin coherence,
• yuqori cavity coupling

talab qilinadi.

Tadqiqotning material-dizayn xulosasi shuki, ideal host butunlay yumshoq ham, butunlay qattiq ham bo‘lmasligi kerak. Nuclear-spin dilution va zararli relaxation pathways ni kamaytiradigan darajada qattiq, biroq pentacene triplet-state geometry o‘zgarishiga ortiqcha strain hosil qilmasdan moslasha oladigan darajada compliant lattice kerak.

Continuous-wave maser oldidagi qo‘shimcha to‘siq

Mualliflar material parametrlari yaxshilanganiga qaramay, haqiqiy CW operation uchun optical pumping hosil qiladigan heat load hanuz muhim texnik to‘siq ekanini qayd etadi.

Laser heating:

• ZFS chastota siljishi,
• STO resonator chastota siljishi

hosil qilishi mumkin.

Shu sabab kelajakda:

• resonator geometriyasi,
• sovutish tizimi,
• excitation geometriyasi,
• invasive pumping sxemalari,
• pastroq pentacene concentrations

kabi parametrlarni optimallashtirish zarurligi qayd etiladi.

Manba va Usul Haqida Izoh

Asl sarlavha: Host-guest Crystal Engineering Tailors the Room Temperature Spin Dynamics in Molecular Quantum Devices

Mualliflar: Ziqiu Huang; Angus Cowley-Semple; Irena Nevjestic; Yifan Yu; Mark Oxborrow; Sam L. Bayliss; Sarah K. Mann; Max Attwood.

Corresponding authors: Mark Oxborrow, Sam L. Bayliss, Sarah K. Mann va Max Attwood manbada corresponding-author e-mail belgilar bilan ko‘rsatilgan.

Muassasa 1: Department of Materials and London Centre for Nanotechnology, Imperial College London, Prince Consort Road, London, SW7 2AZ, UK.

Muassasa 2: James Watt School of Engineering, University of Glasgow, Glasgow, G12 8QQ, UK.

Manba turi: Eksperimental + hisoblashga asoslangan quantum-materials preprint.

Platforma: arXiv.

ArXiv: arXiv:2607.16466v1 [quant-ph].

Ikkinchi tasnif: physics.chem-ph.

Yuborilgan sana: 17 iyul 2026.

Repository DOI: 10.48550/arXiv.2607.16466.

Rasmiy havola: https://arxiv.org/abs/2607.16466

Taqriz holati: 13 noyabr 2026 holatiga ko‘ra tasdiqlangan taqrizdan o‘tgan jurnal versiyasi topilmagan; Imperial College London va University of Glasgow nashr ro‘yxatlarida tadqiqot hanuz arXiv preprint sifatida ko‘rsatilgan.

Litsenziya qaydi: Manba PDF ushbu submission dan kelib chiqadigan har qanday Author Accepted Manuscript versiyasiga CC BY litsenziyasi qo‘llanishini bildiradi. Bu ibora amaldagi arXiv preprint fayli avtomatik ravishda CC BY degani sifatida talqin qilinmagan.

PDF qamrovi: Yuklangan fayl asosiy maqolaga qo‘shimcha ravishda Supporting Information ni ham o‘z ichiga oladi. Supporting Information; crystal photographs, TCSPC fitting, Raman/DFT, additional EPR, Rabi analysis, room-temperature ODMR, relaxation measurements, CW-ODMR linewidth, Hahn echo, population kinetics, maser cooperativity va Q-boost maser setup bo‘limlarini o‘z ichiga oladi.

Data Availability: Manba asosiy matnida “The data underlying this work are available at [URL to be added]” iborasi mavjud. Shu sabab PDF versiyasida final data-repository URL hali to‘ldirilmagan.

Supporting Information havolasi: Asosiy matnda Supporting Information uchun ham “[URL to be added]” placeholder mavjud; biroq foydalanuvchi yuklagan birlashtirilgan PDF ning keyingi sahifalarida Supporting Information mazmuni amalda mavjud.

Moliyalashtirish: EPSRC SPIN-Lab equipment funding EP/P030548/1; UK Research and Innovation MR/W006928/1; UK Research and Innovation EP/W027542/1; Glasgow Engineering Futures Fellowship.

Acknowledgements: Mualliflar SPIN-Lab uskunalarini moliyalashtirish va tegishli UKRI/Fellowship ko‘maklarini qayd etgan.

Manfaatlar to‘qnashuvi: Manba “No conflict of interest to declare” iborasini ishlatadi.

Mualliflar hissasi: Ziqiu Huang methodology, UV/Vis, Raman, EPR, DFT va maser maʼlumotlarining curation/analysis, visualization va original draft ustida ishlagan. Angus Cowley-Semple CW-ODMR data curation, analysis va visualization ni bajargan. Irena Nevjestic EPR supervision va manuscript review/editing taʼminlagan. Yifan Yu Q-boost maser experiment ustida ishlagan. Mark Oxborrow conceptualization va supervision taʼminlagan. Sam L. Bayliss supervision, review/editing va funding acquisition ni bajargan. Sarah K. Mann CW-ODMR/triplet-kinetics data, analysis, visualization, review/editing va funding acquisition da qatnashgan. Max Attwood conceptualization, crystal-growth investigation, overall supervision, review/editing va funding acquisition ni bajargan.

Asosiy eksperimental usullar: UV–vis absorption, TCSPC fluorescence spectroscopy, Raman spectroscopy, X-band transient EPR, CW/pulsed ODMR, optically detected Rabi oscillations, Hahn echo va pulsed maser measurements.

Asosiy hisoblash usullari: B3LYP/6-31G(d,p) DFT vibrational calculations; EasySpin spin-Hamiltonian fitting; coupled population-rate equations; maser cooperativity simulation; COMSOL resonator magnetic-field simulation.

Asosiy qurilma konteksti: Maser experiments high-Q strontium-titanate resonator ichida, TE₀₁δ cavity mode ishlatilgan holda xona haroratida o‘tkazilgan.

Muhim eksperimental cheklov: Pc-d₁₄:PTP-d₁₄ uchun 0,9 mJ natijasi pulsed maser threshold dir; continuous-wave threshold yoki CW output power emas.

Muhim model cheklovi: Continuous-operation simulation da Pc:NAP \(k_{\mathrm{ISC}}\) qiymati adabiyotdan baholangan, Pc:PIC \(k_{\mathrm{ISC}}\) qiymati esa Pc:PTP bilan bir xil deb faraz qilingan. Shu sabab CW suitability xulosasi bevosita faqat o‘lchangan qiymatlardan tashkil topgan mustaqil tajriba emas.

Muhim Raman cheklovi: Pentacene concentration eng ko‘pi bilan 0,1 mol% bo‘lgani sabab host ichidagi pentacene OOP modes eksperimental Raman spectra ichida aniq ajratib bo‘lmagan. DFT va host Raman xususiyatlari mexanistik talqinni qo‘llab-quvvatlash uchun ishlatilgan.

Muhim spin cheklovi: trEPR \(T_{2,\mathrm{Rabi}}\), CW-ODMR line width va zero-field Hahn-echo \(T_2\) turli o‘lchov protokollari hosil qiladigan, o‘zaro bog‘liq, ammo bir xil bo‘lmagan kattaliklardir.