On-Chip Magnetic-Levitation Architecture
Updated 3 December 2025
On-chip magnetic-levitation architectures are microfabricated platforms that generate tailored 3D magnetic field gradients to stably levitate microscopic particles for quantum control and precision sensing.
These systems employ superconducting quadrupole traps, double-loop traps, and AC magnetic Paul traps, with tunable mode frequencies from tens of hertz to tens of kilohertz and varied operating temperatures.
Finite-element modeling confirms excellent agreement with experimental data on trap frequencies, quality factors, and dissipation mitigation, ensuring reliable integration with chip-based readout electronics.
On-chip magnetic-levitation architectures use lithographically patterned microfabricated coils or electrodes to produce field landscapes capable of stably levitating single microscopic particles above solid substrates. These platforms provide three-dimensional field gradients—magnetostatic or time-dependent—tailored for ultra-high mechanical quality factors, motional ground-state cooling, and integration with chip-based readout and feedback electronics. The architectures discussed here include superconducting quadrupole traps for Meissner-state diamagnetic spheres, double-loop planar coil traps, and AC magnetic Paul traps for ferromagnetic particles. Designs accommodate picogram to microgram masses and operate at cryogenic to room temperatures, with mode frequencies spanning tens of hertz up to tens of kilohertz, supporting quantum control and precision inertial sensing (Latorre et al., 2021 , Latorre et al., 2022 , 2002.03868 , Janse et al., 13 Aug 2024 ).
1. Geometric Configurations and Fabrication
Architectures are categorized into three principal geometries: anti-Helmholtz-coil (AHC ) quadrupole traps, planar double-loop (DL) traps, and planar AC magnetic Paul traps (MPT).
AHC Quadrupole Trap:
Implements two vertically displaced planar superconducting coils (typically Nb, thicknesses ∼ \sim ∼ Latorre et al., 2021 , Latorre et al., 2022 ). Each coil features 10–20 windings of 30 µm × \times × ∼ \sim ∼
Double-Loop (DL) Trap:
Co-planar concentric Nb loops with opposing currents, diameters 12–18 µm, wire widths ∼ \sim ∼ ∼ \sim ∼ 2002.03868 ).
Planar AC Magnetic Paul Trap (MPT):
Two planar loops on PCB or silicon, inner radius R 1 = 0.7 R_1=0.7 R 1 = 0.7 R 2 = 1.4 R_2=1.4 R 2 = 1.4 ( + I trap , − ξ I trap , ξ = 2.2 − 2.4 ) (+I_\text{trap}, -\xi I_\text{trap}, \xi=2.2-2.4) ( + I trap , − ξ I trap , ξ = 2.2 − 2.4 ) ∼ \sim ∼ Janse et al., 13 Aug 2024 ).
Materials are selected for high j c j_c j c ∼ \sim ∼ × 1 0 10 \times10^{10} × 1 0 10 1 0 11 10^{11} 1 0 11 2 ^2 2 B c 1 B_{c1} B c 1 λ L \lambda_L λ L
2. Physical Principles and Trap Modeling
Levitation exploits strong field gradients for diamagnetic or paramagnetic force transduction. Quadrupole field patterns—static or oscillatory—produce spatial minima trapping particles in 3D.
Meissner-State Diamagnetism (Superconducting Sphere):
The potential U ( r ) = − χ V ∣ B ( r ) ∣ 2 / ( 2 μ 0 ) U(r)=-\chi V|B(r)|^2/(2\mu_0) U ( r ) = − χ V ∣ B ( r ) ∣ 2 / ( 2 μ 0 ) χ ≈ − 1 \chi\approx-1 χ ≈ − 1 F = − ∇ U F=-\nabla U F = − ∇ U ω i 2 = ( 1 / m ) ∂ 2 U / ∂ x i 2 ∣ r 0 \omega_i^2 = (1/m)\partial^2U/\partial x_i^2|_{r_0} ω i 2 = ( 1/ m ) ∂ 2 U / ∂ x i 2 ∣ r 0 Latorre et al., 2021 , 2002.03868 ).
AC Magnetic Paul Trap (Ferromagnetic Cube):
An oscillating quadrupole field B 1 ( r , t ) = B 1 ′ ′ ( x x ^ + y y ^ − 2 z z ^ ) cos ( Ω t ) \mathbf{B}_1(\mathbf r,t)=B_1''(x\hat{x}+y\hat{y}-2z\hat{z})\cos(\Omega t) B 1 ( r , t ) = B 1 ′′ ( x x ^ + y y ^ − 2 z z ^ ) cos ( Ω t ) q z = 2 μ B 1 ′ ′ / ( m Ω 2 ) q_z = 2\mu B_1''/(m\Omega^2) q z = 2 μ B 1 ′′ / ( m Ω 2 ) ω z = 2 ω x , y = ∣ B 1 ′ ′ ∣ B sat / ( μ 0 ρ m Ω 2 ) \omega_z = 2\omega_{x,y} = |B_1''|B_\text{sat}/(\mu_0\rho_m \Omega \sqrt{2}) ω z = 2 ω x , y = ∣ B 1 ′′ ∣ B sat / ( μ 0 ρ m Ω 2 ) Janse et al., 13 Aug 2024 ).
Finite-element modeling (FEM , COMSOL Multiphysics) solves the Maxwell–London equations, incorporates finite λ L \lambda_L λ L B ( x , y , z ) B(x,y,z) B ( x , y , z ) ∼ 1 0 5 \sim10^5 ∼ 1 0 5 1 0 6 10^6 1 0 6 2002.03868 ).
3. Experimental Parameters and Mode Characterization
Static Quadrupole Superconducting Trap:
Typical coil currents I = 0.1 I=0.1 I = 0.1 G ∼ 1 0 4 G\sim10^4 G ∼ 1 0 4 U 0 ∼ 1 0 − 17 U_0\sim10^{-17} U 0 ∼ 1 0 − 17 ≫ k B \gg k_B ≫ k B K ) . M e a s u r e d t r a p f r e q u e n c i e s f o r 48 – 50 µ m P b / S n P b s p h e r e s a t K). Measured trap frequencies for 48–50 µm Pb/SnPb spheres at K ) . M e a s u re d t r a p f re q u e n c i es f or 48–50 µ m P b / S n P b s p h eres a t A : A: A : – – – H z , Hz, Hz , H z , Hz, Hz , – – – H z ( < a h r e f = " / p a p e r s / 2210.13451 " t i t l e = " " r e l = " n o f o l l o w " d a t a − t u r b o = " f a l s e " c l a s s = " a s s i s t a n t − l i n k " x − d a t a x − t o o l t i p . r a w = " " > L a t o r r e e t a l . , 2022 < / a > , < a h r e f = " / p a p e r s / 2109.15071 " t i t l e = " " r e l = " n o f o l l o w " d a t a − t u r b o = " f a l s e " c l a s s = " a s s i s t a n t − l i n k " x − d a t a x − t o o l t i p . r a w = " " > L a t o r r e e t a l . , 2021 < / a > ) . < / l i > < l i > M o t i o n a l m o d e q u a l i t y f a c t o r s Hz (<a href="/papers/2210.13451" title="" rel="nofollow" data-turbo="false" class="assistant-link" x-data x-tooltip.raw="">Latorre et al., 2022</a>, <a href="/papers/2109.15071" title="" rel="nofollow" data-turbo="false" class="assistant-link" x-data x-tooltip.raw="">Latorre et al., 2021</a>).</li>
<li>Motional mode quality factors Hz ( < ah re f = "/ p a p ers /2210.13451" t i tl e = "" re l = " n o f o ll o w " d a t a − t u r b o = " f a l se " c l a ss = " a ss i s t an t − l ink " x − d a t a x − t oo lt i p . r a w = "" > L a t orree t a l . , 2022 < / a > , < ah re f = "/ p a p ers /2109.15071" t i tl e = "" re l = " n o f o ll o w " d a t a − t u r b o = " f a l se " c l a ss = " a ss i s t an t − l ink " x − d a t a x − t oo lt i p . r a w = "" > L a t orree t a l . , 2021 < / a > ) . < / l i >< l i > M o t i o na l m o d e q u a l i t y f a c t ors – – – l i m i t e d b y e d d y c u r r e n t d a m p i n g . T r a p f r e q u e n c i e s a r e t u n a b l e limited by eddy current damping. Trap frequencies are tunable l imi t e d b ye dd yc u rre n t d am p in g . T r a p f re q u e n c i es a re t u nab l e i n t h e 30 – 160 H z r a n g e . D u f f i n g n o n l i n e a r i t i e s a n d i n t e r − m o d e c o u p l i n g a r e q u a n t i f i e d u s i n g F E M , w i t h q u a r t i c c o e f f i c i e n t s in the 30–160 Hz range. Duffing nonlinearities and inter-mode coupling are quantified using FEM, with quartic coefficients in t h e 30–160 Hzr an g e . D u ff in g n o n l in e a r i t i es an d in t er − m o d eco u pl in g a re q u an t i f i e d u s in g FEM , w i t h q u a r t i ccoe ff i c i e n t s – – – m m m s s s ( < a h r e f = " / p a p e r s / 2210.13451 " t i t l e = " " r e l = " n o f o l l o w " d a t a − t u r b o = " f a l s e " c l a s s = " a s s i s t a n t − l i n k " x − d a t a x − t o o l t i p . r a w = " " > L a t o r r e e t a l . , 2022 < / a > ) . < / l i > < / u l > < / l i > < l i > < s t r o n g > A H C a n d D L T r a p s ( M i c r o s c a l e ) : < / s t r o n g > < u l > < l i > A H C t r a p s ( (<a href="/papers/2210.13451" title="" rel="nofollow" data-turbo="false" class="assistant-link" x-data x-tooltip.raw="">Latorre et al., 2022</a>).</li>
</ul></li>
<li><strong>AHC and DL Traps (Microscale):</strong>
<ul>
<li>AHC traps ( ( < ah re f = "/ p a p ers /2210.13451" t i tl e = "" re l = " n o f o ll o w " d a t a − t u r b o = " f a l se " c l a ss = " a ss i s t an t − l ink " x − d a t a x − t oo lt i p . r a w = "" > L a t orree t a l . , 2022 < / a > ) . < / l i >< / u l >< / l i >< l i >< s t ro n g > A H C an d D L T r a p s ( M i crosc a l e ) :< / s t ro n g >< u l >< l i > A H Ct r a p s ( µ m s p h e r e s , µm spheres, µ m s p h eres , A / m A/m A / m ) p r o d u c e ) produce ) p ro d u ce k H z , kHz, k Hz , k H z , kHz, k Hz , k H z . D L t r a p s ( 10 µ m s p h e r e ) y i e l d kHz. DL traps (10 µm sphere) yield k Hz . D L t r a p s ( 10 µ m s p h ere ) y i e l d H z ( < a h r e f = " / p a p e r s / 2002.03868 " t i t l e = " " r e l = " n o f o l l o w " d a t a − t u r b o = " f a l s e " c l a s s = " a s s i s t a n t − l i n k " x − d a t a x − t o o l t i p . r a w = " " > 2002.03868 < / a > ) . < / l i > < l i > T r a p f r e q u e n c y s c a l i n g i s c a p t u r e d b y Hz (<a href="/papers/2002.03868" title="" rel="nofollow" data-turbo="false" class="assistant-link" x-data x-tooltip.raw="">2002.03868</a>).</li>
<li>Trap frequency scaling is captured by Hz ( < ah re f = "/ p a p ers /2002.03868" t i tl e = "" re l = " n o f o ll o w " d a t a − t u r b o = " f a l se " c l a ss = " a ss i s t an t − l ink " x − d a t a x − t oo lt i p . r a w = "" > 2002.03868 < / a > ) . < / l i >< l i > T r a p f re q u e n cysc a l in g i sc a pt u re d b y . < / l i > < / u l > < / l i > < l i > < s t r o n g > A C M a g n e t i c P a u l T r a p ( R o o m − T e m p e r a t u r e F e r r o m a g n e t ) : < / s t r o n g > < u l > < l i > 250 µ m − e d g e c u b e , .</li>
</ul></li>
<li><strong>AC Magnetic Paul Trap (Room-Temperature Ferromagnet):</strong>
<ul>
<li>250 µm-edge cube, . < / l i >< / u l >< / l i >< l i >< s t ro n g > A CM a g n e t i c P a u lT r a p ( R oo m − T e m p er a t u re F erro ma g n e t ) :< / s t ro n g >< u l >< l i > 250 µ m − e d g ec u b e , A , A, A , H z , y i e l d s Hz, yields Hz , y i e l d s H z . L i b r a t i o n a l m o d e s Hz. Librational modes Hz . L ib r a t i o na l m o d es H z . Q − f a c t o r s p e a k a t Hz. Q-factors peak at Hz . Q − f a c t ors p e aka t , d o m i n a t e d b y e d d y c u r r e n t s ; v i b r a t i o n a l , dominated by eddy currents; vibrational , d o mina t e d b ye dd yc u rre n t s ; v ib r a t i o na l – – – ( < a h r e f = " / p a p e r s / 2408.06838 " t i t l e = " " r e l = " n o f o l l o w " d a t a − t u r b o = " f a l s e " c l a s s = " a s s i s t a n t − l i n k " x − d a t a x − t o o l t i p . r a w = " " > J a n s e e t a l . , 13 A u g 2024 < / a > ) . < / l i > < / u l > < / l i > < / u l > < h 2 c l a s s = ′ p a p e r − h e a d i n g ′ i d = ′ i n t e g r a t e d − r e a d o u t − a n d − c o u p l i n g − t e c h n i q u e s ′ > 4. I n t e g r a t e d R e a d o u t a n d C o u p l i n g T e c h n i q u e s < / h 2 > < p > C h i p − b a s e d p l a t f o r m s s u p p o r t i n t e g r a t i o n o f s u p e r c o n d u c t i n g a n d m a g n e t i c r e a d o u t s . < / p > < u l > < l i > < s t r o n g > D C − S Q U I D M a g n e t o m e t r y : < / s t r o n g > < u l > < l i > S u p e r c o n d u c t i n g p i c k u p l o o p s ( L (<a href="/papers/2408.06838" title="" rel="nofollow" data-turbo="false" class="assistant-link" x-data x-tooltip.raw="">Janse et al., 13 Aug 2024</a>).</li>
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<h2 class='paper-heading' id='integrated-readout-and-coupling-techniques'>4. Integrated Readout and Coupling Techniques</h2>
<p>Chip-based platforms support integration of superconducting and magnetic readouts.</p>
<ul>
<li><strong>DC-SQUID Magnetometry:</strong>
<ul>
<li>Superconducting pickup loops (L ( < ah re f = "/ p a p ers /2408.06838" t i tl e = "" re l = " n o f o ll o w " d a t a − t u r b o = " f a l se " c l a ss = " a ss i s t an t − l ink " x − d a t a x − t oo lt i p . r a w = "" > J an see t a l . , 13 A ug 2024 < / a > ) . < / l i >< / u l >< / l i >< / u l >< h 2 c l a ss = ′ p a p er − h e a d in g ′ i d = ′ in t e g r a t e d − re a d o u t − an d − co u pl in g − t ec hni q u e s ′ > 4. I n t e g r a t e d R e a d o u t an d C o u pl in g T ec hni q u es < / h 2 >< p > C hi p − ba se d pl a t f or m ss u pp or t in t e g r a t i o n o f s u p erco n d u c t in g an d ma g n e t i cre a d o u t s . < / p >< u l >< l i >< s t ro n g > D C − SQ U I D M a g n e t o m e t ry :< / s t ro n g >< u l >< l i > S u p erco n d u c t in g p i c k u pl oo p s ( L n H ) , o f f s e t b y nH), offset by n H ) , o ff se t b y µ m , c o u p l e d t o c o m m e r c i a l D C − S Q U I D s ( i n p u t µm, coupled to commercial DC-SQUIDs (input µ m , co u pl e d t oco mm erc ia l D C − SQ U I Ds ( in p u t n H , m u t u a l nH, mutual n H , m u t u a l n H ) . F l u x t r a n s f e r e f f i c i e n c y nH). Flux transfer efficiency n H ) . Fl ux t r an s f ere ff i c i e n cy ; n o i s e f l o o r ; noise floor ; n o i se f l oor m m m / H z /Hz / Hz , d i s p l a c e m e n t s e n s i t i v i t y , displacement sensitivity , d i s pl a ce m e n t se n s i t i v i t y n m / H z nm/Hz nm / Hz ( x ) , (x), ( x ) , n m / H z nm/Hz nm / Hz ( y ) , (y), ( y ) , n m / H z nm/Hz nm / Hz ( z ) . I m p r o v e d m a t c h i n g a n d p e r s i s t e n t − c u r r e n t t r a p s w i l l a p p r o a c h t h e i n t r i n s i c S Q U I D n o i s e (z). Improved matching and persistent-current traps will approach the intrinsic SQUID noise ( z ) . I m p ro v e d ma t c hin g an d p ers i s t e n t − c u rre n tt r a p s w i ll a pp ro a c h t h e in t r in s i c SQ U I D n o i se / H z /Hz / Hz ( < a h r e f = " / p a p e r s / 2210.13451 " t i t l e = " " r e l = " n o f o l l o w " d a t a − t u r b o = " f a l s e " c l a s s = " a s s i s t a n t − l i n k " x − d a t a x − t o o l t i p . r a w = " " > L a t o r r e e t a l . , 2022 < / a > ) . < / l i > < / u l > < / l i > < l i > < s t r o n g > P r o s p e c t i v e H y b r i d R e a d o u t s : < / s t r o n g > < u l > < l i > O n − c h i p s u p e r c o n d u c t i n g m i c r o w a v e c a v i t i e s ( s i d e b a n d c o o l i n g , g r o u n d − s t a t e c o o l i n g (<a href="/papers/2210.13451" title="" rel="nofollow" data-turbo="false" class="assistant-link" x-data x-tooltip.raw="">Latorre et al., 2022</a>).</li>
</ul></li>
<li><strong>Prospective Hybrid Readouts:</strong>
<ul>
<li>On-chip superconducting microwave cavities (sideband cooling, ground-state cooling ( < ah re f = "/ p a p ers /2210.13451" t i tl e = "" re l = " n o f o ll o w " d a t a − t u r b o = " f a l se " c l a ss = " a ss i s t an t − l ink " x − d a t a x − t oo lt i p . r a w = "" > L a t orree t a l . , 2022 < / a > ) . < / l i >< / u l >< / l i >< l i >< s t ro n g > P ros p ec t i v eHy b r i d R e a d o u t s :< / s t ro n g >< u l >< l i > O n − c hi p s u p erco n d u c t in g mi cro w a v ec a v i t i es ( s i d e ban d coo l in g , g ro u n d − s t a t ecoo l in g ) , v e c t o r − r e s o l v e d i n e r t i a l s e n s i n g a r r a y s , a n d c o u p l i n g t o N V c e n t e r s f o r s p i n − m e c h a n i c s ( < a h r e f = " / p a p e r s / 2408.06838 " t i t l e = " " r e l = " n o f o l l o w " d a t a − t u r b o = " f a l s e " c l a s s = " a s s i s t a n t − l i n k " x − d a t a x − t o o l t i p . r a w = " " > J a n s e e t a l . , 13 A u g 2024 < / a > ) . < / l i > < / u l > < / l i > < / u l > < h 2 c l a s s = ′ p a p e r − h e a d i n g ′ i d = ′ d i s s i p a t i o n − s t a b i l i t y − a n d − n o i s e − m i t i g a t i o n ′ > 5. D i s s i p a t i o n , S t a b i l i t y , a n d N o i s e M i t i g a t i o n < / h 2 > < p > S u p e r c o n d u c t i n g t r a p s a t c r y o g e n i c t e m p e r a t u r e ( ), vector-resolved inertial sensing arrays, and coupling to NV centers for spin-mechanics (<a href="/papers/2408.06838" title="" rel="nofollow" data-turbo="false" class="assistant-link" x-data x-tooltip.raw="">Janse et al., 13 Aug 2024</a>).</li>
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<h2 class='paper-heading' id='dissipation-stability-and-noise-mitigation'>5. Dissipation, Stability, and Noise Mitigation</h2>
<p>Superconducting traps at cryogenic temperature ( ) , v ec t or − reso l v e d in er t ia l se n s in g a rr a ys , an d co u pl in g t o N V ce n t ers f ors p in − m ec hani cs ( < ah re f = "/ p a p ers /2408.06838" t i tl e = "" re l = " n o f o ll o w " d a t a − t u r b o = " f a l se " c l a ss = " a ss i s t an t − l ink " x − d a t a x − t oo lt i p . r a w = "" > J an see t a l . , 13 A ug 2024 < / a > ) . < / l i >< / u l >< / l i >< / u l >< h 2 c l a ss = ′ p a p er − h e a d in g ′ i d = ′ d i ss i p a t i o n − s t abi l i t y − an d − n o i se − mi t i g a t i o n ′ > 5. D i ss i p a t i o n , St abi l i t y , an d N o i se M i t i g a t i o n < / h 2 >< p > S u p erco n d u c t in g t r a p s a t cryo g e ni c t e m p er a t u re ( m K – 4 K ) e x h i b i t m i n i m a l i n t r i n s i c d i s s i p a t i o n . L i f e t i m e s e x c e e d d a y s i n t h e a b s e n c e o f i l l u m i n a t i o n . < / p > < u l > < l i > < s t r o n g > P r i m a r y D i s s i p a t i o n C h a n n e l s : < / s t r o n g > < u l > < l i > E d d y c u r r e n t s i n n e a r b y n o r m a l m e t a l s , r e s i s t i v e h e a t i n g o f c o i l t r a c k s , t e c h n i c a l h e a t i n g o r f l u x t r a p p i n g f r o m o p t i c a l i l l u m i n a t i o n ( t r a p p e d p a r t i c l e s r e l e a s e d a f t e r mK–4 K) exhibit minimal intrinsic dissipation. Lifetimes exceed days in the absence of illumination.</p>
<ul>
<li><strong>Primary Dissipation Channels:</strong>
<ul>
<li>Eddy currents in nearby normal metals, resistive heating of coil tracks, technical heating or flux trapping from optical illumination (trapped particles released after m K –4 K ) e x hibi t minima l in t r in s i c d i ss i p a t i o n . L i f e t im ese x cee dd a ys in t h e ab se n ceo f i ll u mina t i o n . < / p >< u l >< l i >< s t ro n g > P r ima ryD i ss i p a t i o n C hann e l s :< / s t ro n g >< u l >< l i > E dd yc u rre n t s inn e a r b y n or ma l m e t a l s , res i s t i v e h e a t in g o f co i lt r a c k s , t ec hni c a l h e a t in g or f l ux t r a pp in g f ro m o pt i c a l i ll u mina t i o n ( t r a pp e d p a r t i c l esre l e a se d a f t er s c o n t i n u o u s e x p o s u r e ) ( < a h r e f = " / p a p e r s / 2109.15071 " t i t l e = " " r e l = " n o f o l l o w " d a t a − t u r b o = " f a l s e " c l a s s = " a s s i s t a n t − l i n k " x − d a t a x − t o o l t i p . r a w = " " > L a t o r r e e t a l . , 2021 < / a > , < a h r e f = " / p a p e r s / 2408.06838 " t i t l e = " " r e l = " n o f o l l o w " d a t a − t u r b o = " f a l s e " c l a s s = " a s s i s t a n t − l i n k " x − d a t a x − t o o l t i p . r a w = " " > J a n s e e t a l . , 13 A u g 2024 < / a > ) . < / l i > < l i > I n A C P a u l t r a p s , e d d y − c u r r e n t d a m p i n g d o m i n a t e s o v e r < a h r e f = " h t t p s : / / w w w . e m e r g e n t m i n d . c o m / t o p i c s / g e n e t i c − a l g o r i t h m s − g a s " t i t l e = " " r e l = " n o f o l l o w " d a t a − t u r b o = " f a l s e " c l a s s = " a s s i s t a n t − l i n k " x − d a t a x − t o o l t i p . r a w = " " > g a s < / a > d a m p i n g . P r e s s u r e d e p e n d e n c e i s w e a k ( s continuous exposure) (<a href="/papers/2109.15071" title="" rel="nofollow" data-turbo="false" class="assistant-link" x-data x-tooltip.raw="">Latorre et al., 2021</a>, <a href="/papers/2408.06838" title="" rel="nofollow" data-turbo="false" class="assistant-link" x-data x-tooltip.raw="">Janse et al., 13 Aug 2024</a>).</li>
<li>In AC Paul traps, eddy-current damping dominates over <a href="https://www.emergentmind.com/topics/genetic-algorithms-gas" title="" rel="nofollow" data-turbo="false" class="assistant-link" x-data x-tooltip.raw="">gas</a> damping. Pressure dependence is weak ( sco n t in u o u se x p os u re ) ( < ah re f = "/ p a p ers /2109.15071" t i tl e = "" re l = " n o f o ll o w " d a t a − t u r b o = " f a l se " c l a ss = " a ss i s t an t − l ink " x − d a t a x − t oo lt i p . r a w = "" > L a t orree t a l . , 2021 < / a > , < ah re f = "/ p a p ers /2408.06838" t i tl e = "" re l = " n o f o ll o w " d a t a − t u r b o = " f a l se " c l a ss = " a ss i s t an t − l ink " x − d a t a x − t oo lt i p . r a w = "" > J an see t a l . , 13 A ug 2024 < / a > ) . < / l i >< l i > I n A CP a u lt r a p s , e dd y − c u rre n t d am p in g d o mina t eso v er < ah re f = " h ttp s : // www . e m er g e n t min d . co m / t o p i cs / g e n e t i c − a l g or i t hm s − g a s " t i tl e = "" re l = " n o f o ll o w " d a t a − t u r b o = " f a l se " c l a ss = " a ss i s t an t − l ink " x − d a t a x − t oo lt i p . r a w = "" > g a s < / a > d am p in g . P ress u re d e p e n d e n ce i s w e ak ( b a r e l y i n c r e a s e s f r o m barely increases from ba re l y in cre a ses f ro m b a r t o bar to ba r t o m b a r ) . < / l i > < / u l > < / l i > < l i > < s t r o n g > M i t i g a t i o n S t r a t e g i e s : < / s t r o n g > < u l > < l i > U s e o f s u p e r c o n d u c t i n g m i c r o s t r i p s , s u p e r c o n d u c t i n g s h i e l d i n g ( N b / C r y o p e r m ) , m e c h a n i c a l i s o l a t i o n , r e m o v a l o f c o n d u c t i v e c o a t i n g s o n p a r t i c l e s , c a r e f u l m a t c h i n g o f c o i l a p e r t u r e s a n d s e p a r a t i o n , p e r s i s t e n t − c u r r e n t o p e r a t i o n t o s u p p r e s s c u r r e n t − n o i s e − i n d u c e d f l i c k e r ( < a h r e f = " / p a p e r s / 2210.13451 " t i t l e = " " r e l = " n o f o l l o w " d a t a − t u r b o = " f a l s e " c l a s s = " a s s i s t a n t − l i n k " x − d a t a x − t o o l t i p . r a w = " " > L a t o r r e e t a l . , 2022 < / a > , < a h r e f = " / p a p e r s / 2408.06838 " t i t l e = " " r e l = " n o f o l l o w " d a t a − t u r b o = " f a l s e " c l a s s = " a s s i s t a n t − l i n k " x − d a t a x − t o o l t i p . r a w = " " > J a n s e e t a l . , 13 A u g 2024 < / a > ) . < / l i > < / u l > < / l i > < / u l > < h 2 c l a s s = ′ p a p e r − h e a d i n g ′ i d = ′ f u n c t i o n a l − i m p l i c a t i o n s − a n d − a p p l i c a t i o n s ′ > 6. F u n c t i o n a l I m p l i c a t i o n s a n d A p p l i c a t i o n s < / h 2 > < p > C h i p − b a s e d m a g n e t i c − l e v i t a t i o n e n a b l e s q u a n t u m o p t o m e c h a n i c s , i n e r t i a l a n d f o r c e s e n s i n g , a n d f u n d a m e n t a l m a c r o s c a l e q u a n t u m t e s t s . < / p > < u l > < l i > < s t r o n g > Q u a n t u m G r o u n d − S t a t e C o o l i n g a n d C o n t r o l : < / s t r o n g > < u l > < l i > F E M m o d e l s p r e d i c t c h i p − s c a l e t r a p s w i t h mbar).</li>
</ul></li>
<li><strong>Mitigation Strategies:</strong>
<ul>
<li>Use of superconducting microstrips, superconducting shielding (Nb/Cryoperm), mechanical isolation, removal of conductive coatings on particles, careful matching of coil apertures and separation, persistent-current operation to suppress current-noise-induced flicker (<a href="/papers/2210.13451" title="" rel="nofollow" data-turbo="false" class="assistant-link" x-data x-tooltip.raw="">Latorre et al., 2022</a>, <a href="/papers/2408.06838" title="" rel="nofollow" data-turbo="false" class="assistant-link" x-data x-tooltip.raw="">Janse et al., 13 Aug 2024</a>).</li>
</ul></li>
</ul>
<h2 class='paper-heading' id='functional-implications-and-applications'>6. Functional Implications and Applications</h2>
<p>Chip-based magnetic-levitation enables quantum optomechanics, inertial and force sensing, and fundamental macroscale quantum tests.</p>
<ul>
<li><strong>Quantum Ground-State Cooling and Control:</strong>
<ul>
<li>FEM models predict chip-scale traps with mba r ) . < / l i >< / u l >< / l i >< l i >< s t ro n g > M i t i g a t i o n St r a t e g i es :< / s t ro n g >< u l >< l i > U seo f s u p erco n d u c t in g mi cros t r i p s , s u p erco n d u c t in g s hi e l d in g ( N b / C ryo p er m ) , m ec hani c a l i so l a t i o n , re m o v a l o f co n d u c t i v eco a t in g so n p a r t i c l es , c a re f u l ma t c hin g o f co i l a p er t u res an d se p a r a t i o n , p ers i s t e n t − c u rre n t o p er a t i o n t os u pp ressc u rre n t − n o i se − in d u ce df l i c k er ( < ah re f = "/ p a p ers /2210.13451" t i tl e = "" re l = " n o f o ll o w " d a t a − t u r b o = " f a l se " c l a ss = " a ss i s t an t − l ink " x − d a t a x − t oo lt i p . r a w = "" > L a t orree t a l . , 2022 < / a > , < ah re f = "/ p a p ers /2408.06838" t i tl e = "" re l = " n o f o ll o w " d a t a − t u r b o = " f a l se " c l a ss = " a ss i s t an t − l ink " x − d a t a x − t oo lt i p . r a w = "" > J an see t a l . , 13 A ug 2024 < / a > ) . < / l i >< / u l >< / l i >< / u l >< h 2 c l a ss = ′ p a p er − h e a d in g ′ i d = ′ f u n c t i o na l − im pl i c a t i o n s − an d − a ppl i c a t i o n s ′ > 6. F u n c t i o na l I m pl i c a t i o n s an d A ppl i c a t i o n s < / h 2 >< p > C hi p − ba se d ma g n e t i c − l e v i t a t i o n e nab l es q u an t u m o pt o m ec hani cs , in er t ia l an df orcese n s in g , an df u n d am e n t a l ma crosc a l e q u an t u m t es t s . < / p >< u l >< l i >< s t ro n g > Q u an t u m G ro u n d − St a t e C oo l in g an d C o n t ro l :< / s t ro n g >< u l >< l i > FEM m o d e l s p re d i c t c hi p − sc a l e t r a p s w i t h e n a b l i n g M H z − s c a l e c a v i t y c o u p l i n g ; f e e d b a c k / s i d e b a n d p r o t o c o l s e x p e c t e d t o r e a c h m o t i o n a l g r o u n d s t a t e i n enabling MHz-scale cavity coupling; feedback/sideband protocols expected to reach motional ground state in e nab l in g M Hz − sc a l ec a v i t yco u pl in g ; f ee d ba c k / s i d e ban d p ro t oco l se x p ec t e d t ore a c hm o t i o na l g ro u n d s t a t e in m s . L o w n o i s e a n d h i g h ms. Low noise and high m s . L o w n o i se an d hi g h o p e n a c c e s s t o m a c r o s c a l e q u a n t u m s u p e r p o s i t i o n s a n d t e s t s o f c o l l a p s e m o d e l s , d e c o h e r e n c e , a n d g r a v i t y ( < a h r e f = " / p a p e r s / 2210.13451 " t i t l e = " " r e l = " n o f o l l o w " d a t a − t u r b o = " f a l s e " c l a s s = " a s s i s t a n t − l i n k " x − d a t a x − t o o l t i p . r a w = " " > L a t o r r e e t a l . , 2022 < / a > , < a h r e f = " / p a p e r s / 2002.03868 " t i t l e = " " r e l = " n o f o l l o w " d a t a − t u r b o = " f a l s e " c l a s s = " a s s i s t a n t − l i n k " x − d a t a x − t o o l t i p . r a w = " " > 2002.03868 < / a > ) . < / l i > < / u l > < / l i > < l i > < s t r o n g > P r e c i s i o n S e n s i n g : < / s t r o n g > < u l > < l i > S e n s i t i v i t y open access to macroscale quantum superpositions and tests of collapse models, decoherence, and gravity (<a href="/papers/2210.13451" title="" rel="nofollow" data-turbo="false" class="assistant-link" x-data x-tooltip.raw="">Latorre et al., 2022</a>, <a href="/papers/2002.03868" title="" rel="nofollow" data-turbo="false" class="assistant-link" x-data x-tooltip.raw="">2002.03868</a>).</li>
</ul></li>
<li><strong>Precision Sensing:</strong>
<ul>
<li>Sensitivity o p e na ccess t o ma crosc a l e q u an t u m s u p er p os i t i o n s an d t es t so f co ll a p se m o d e l s , d eco h ere n ce , an d g r a v i t y ( < ah re f = "/ p a p ers /2210.13451" t i tl e = "" re l = " n o f o ll o w " d a t a − t u r b o = " f a l se " c l a ss = " a ss i s t an t − l ink " x − d a t a x − t oo lt i p . r a w = "" > L a t orree t a l . , 2022 < / a > , < ah re f = "/ p a p ers /2002.03868" t i tl e = "" re l = " n o f o ll o w " d a t a − t u r b o = " f a l se " c l a ss = " a ss i s t an t − l ink " x − d a t a x − t oo lt i p . r a w = "" > 2002.03868 < / a > ) . < / l i >< / u l >< / l i >< l i >< s t ro n g > P rec i s i o n S e n s in g :< / s t ro n g >< u l >< l i > S e n s i t i v i t y w i t h with w i t h k g , kg, k g , H z , Hz, Hz , N / H z N/Hz N / Hz g i v e s gives g i v es / H z /Hz / Hz ( < a h r e f = " / p a p e r s / 2210.13451 " t i t l e = " " r e l = " n o f o l l o w " d a t a − t u r b o = " f a l s e " c l a s s = " a s s i s t a n t − l i n k " x − d a t a x − t o o l t i p . r a w = " " > L a t o r r e e t a l . , 2022 < / a > ) . C h i p a r r a y s a l l o w v e c t o r − r e s o l v e d i n e r t i a l / g r a v i t a t i o n a l s e n s i n g a n d t e s t s o f s h o r t − r a n g e f o r c e s . < / l i > < / u l > < / l i > < l i > < s t r o n g > Q u a n t u m − M a g n e t i c C o u p l i n g : < / s t r o n g > < u l > < l i > O n − c h i p A C M P T s f o r m i c r o n − s c a l e f e r r o m a g n e t i c g r a i n s o f f e r M H z l i b r a t i o n a l f r e q u e n c i e s , d i r e c t m a g n e t i c c o u p l i n g t o s p i n s ( N V c e n t e r s ) , a n d h i g h p h o n o n i c c o u p l i n g s t r e n g t h s (<a href="/papers/2210.13451" title="" rel="nofollow" data-turbo="false" class="assistant-link" x-data x-tooltip.raw="">Latorre et al., 2022</a>). Chip arrays allow vector-resolved inertial/gravitational sensing and tests of short-range forces.</li>
</ul></li>
<li><strong>Quantum-Magnetic Coupling:</strong>
<ul>
<li>On-chip AC MPTs for micron-scale ferromagnetic grains offer MHz librational frequencies, direct magnetic coupling to spins (NV centers), and high phononic coupling strengths ( < ah re f = "/ p a p ers /2210.13451" t i tl e = "" re l = " n o f o ll o w " d a t a − t u r b o = " f a l se " c l a ss = " a ss i s t an t − l ink " x − d a t a x − t oo lt i p . r a w = "" > L a t orree t a l . , 2022 < / a > ) . C hi p a rr a ys a ll o w v ec t or − reso l v e d in er t ia l / g r a v i t a t i o na l se n s in g an d t es t so f s h or t − r an g e f orces . < / l i >< / u l >< / l i >< l i >< s t ro n g > Q u an t u m − M a g n e t i c C o u pl in g :< / s t ro n g >< u l >< l i > O n − c hi p A CMPT s f or mi cro n − sc a l e f erro ma g n e t i c g r ain so ff er M Hz l ib r a t i o na l f re q u e n c i es , d i rec t ma g n e t i cco u pl in g t os p in s ( N V ce n t ers ) , an d hi g h p h o n o ni cco u pl in g s t re n g t h s – – – k H z ( < a h r e f = " / p a p e r s / 2408.06838 " t i t l e = " " r e l = " n o f o l l o w " d a t a − t u r b o = " f a l s e " c l a s s = " a s s i s t a n t − l i n k " x − d a t a x − t o o l t i p . r a w = " " > J a n s e e t a l . , 13 A u g 2024 < / a > ) . < / l i > < / u l > < / l i > < l i > < s t r o n g > S c a l a b i l i t y a n d I n t e g r a t i o n : < / s t r o n g > < u l > < l i > S c a l i n g t o s u b − m i c r o n p a r t i c l e s r e q u i r e s i n c r e a s i n g kHz (<a href="/papers/2408.06838" title="" rel="nofollow" data-turbo="false" class="assistant-link" x-data x-tooltip.raw="">Janse et al., 13 Aug 2024</a>).</li>
</ul></li>
<li><strong>Scalability and Integration:</strong>
<ul>
<li>Scaling to sub-micron particles requires increasing k Hz ( < ah re f = "/ p a p ers /2408.06838" t i tl e = "" re l = " n o f o ll o w " d a t a − t u r b o = " f a l se " c l a ss = " a ss i s t an t − l ink " x − d a t a x − t oo lt i p . r a w = "" > J an see t a l . , 13 A ug 2024 < / a > ) . < / l i >< / u l >< / l i >< l i >< s t ro n g > S c a l abi l i t y an d I n t e g r a t i o n :< / s t ro n g >< u l >< l i > S c a l in g t os u b − mi cro n p a r t i c l esre q u i res in cre a s in g t o to t o T / m T/m T / m — s u p e r c o n d u c t i n g t r a c k s o r p u l s e d o p e r a t i o n f o r c u r r e n t d e n s i t y , c r y o g e n i c a n c h o r i n g , a n d m i c r o f l u i d i c o r d i e l e c t r o p h o r e t i c o n − c h i p l o a d i n g a r e n e c e s s a r y . < / l i > < / u l > < / l i > < / u l > < h 2 c l a s s = ′ p a p e r − h e a d i n g ′ i d = ′ t a b l e − k e y − e x p e r i m e n t a l − f e a t u r e s − o f − r e p r e s e n t a t i v e − a r c h i t e c t u r e s ′ > T a b l e : K e y E x p e r i m e n t a l F e a t u r e s o f R e p r e s e n t a t i v e A r c h i t e c t u r e s < / h 2 > < d i v c l a s s = ′ o v e r f l o w − x − a u t o m a x − w − f u l l m y − 4 ′ > < t a b l e c l a s s = ′ t a b l e b o r d e r − c o l l a p s e w − f u l l ′ s t y l e = ′ t a b l e − l a y o u t : f i x e d ′ > < t h e a d > < t r > < t h > A r c h i t e c t u r e < / t h > < t h > T y p i c a l P a r t i c l e S i z e < / t h > < t h > T r a p F r e q u e n c i e s < / t h > < t h > Q u a l i t y F a c t o r < / t h > < / t r > < / t h e a d > < t b o d y > < t r > < t d > A H C Q u a d r u p o l e T r a p < / t d > < t d > —superconducting tracks or pulsed operation for current density, cryogenic anchoring, and microfluidic or dielectrophoretic on-chip loading are necessary.</li>
</ul></li>
</ul>
<h2 class='paper-heading' id='table-key-experimental-features-of-representative-architectures'>Table: Key Experimental Features of Representative Architectures</h2><div class='overflow-x-auto max-w-full my-4'><table class='table border-collapse w-full' style='table-layout: fixed'><thead><tr>
<th>Architecture</th>
<th>Typical Particle Size</th>
<th>Trap Frequencies</th>
<th>Quality Factor</th>
</tr>
</thead><tbody><tr>
<td>AHC Quadrupole Trap</td>
<td> — s u p erco n d u c t in g t r a c k sor p u l se d o p er a t i o n f orc u rre n t d e n s i t y , cryo g e ni c an c h or in g , an d mi cro f l u i d i cor d i e l ec t ro p h ore t i co n − c hi pl o a d in g a re n ecess a ry . < / l i >< / u l >< / l i >< / u l >< h 2 c l a ss = ′ p a p er − h e a d in g ′ i d = ′ t ab l e − k ey − e x p er im e n t a l − f e a t u res − o f − re p rese n t a t i v e − a rc hi t ec t u re s ′ > T ab l e : Key E x p er im e n t a lF e a t u reso f R e p rese n t a t i v e A rc hi t ec t u res < / h 2 >< d i v c l a ss = ′ o v er f l o w − x − a u t o ma x − w − f u ll m y − 4 ′ >< t ab l ec l a ss = ′ t ab l e b or d er − co ll a p se w − f u l l ′ s t y l e = ′ t ab l e − l a yo u t : f i x e d ′ >< t h e a d >< t r >< t h > A rc hi t ec t u re < / t h >< t h > T y p i c a lP a r t i c l e S i ze < / t h >< t h > T r a pF re q u e n c i es < / t h >< t h > Q u a l i t y F a c t or < / t h >< / t r >< / t h e a d >< t b o d y >< t r >< t d > A H CQ u a d r u p o l e T r a p < / t d >< t d > – – – µ m ( P b / S n P b s p h e r e ) < / t d > < t d > µm (Pb/SnPb sphere)</td>
<td> µ m ( P b / S n P b s p h ere ) < / t d >< t d > – – – H z ( e x p ) , u p t o Hz (exp), up to Hz ( e x p ) , u pt o k H z ( F E M ) < / t d > < t d > kHz (FEM)</td>
<td> k Hz ( FEM ) < / t d >< t d > – – – < / t d > < / t r > < t r > < t d > D L T r a p < / t d > < t d > </td>
</tr>
<tr>
<td>DL Trap</td>
<td> < / t d >< / t r >< t r >< t d > D L T r a p < / t d >< t d > µ m ( s p h e r e ) < / t d > < t d > µm (sphere)</td>
<td> µ m ( s p h ere ) < / t d >< t d > – – – H z ( F E M ) < / t d > < t d > S i m i l a r t o A H C < / t d > < / t r > < t r > < t d > P l a n a r A C M P T < / t d > < t d > Hz (FEM)</td>
<td>Similar to AHC</td>
</tr>
<tr>
<td>Planar AC MPT</td>
<td> Hz ( FEM ) < / t d >< t d > S imi l a r t o A H C < / t d >< / t r >< t r >< t d > Pl ana r A CMPT < / t d >< t d > µ m c u b e ( N d F e B ) < / t d > < t d > µm cube (NdFeB)</td>
<td> µ m c u b e ( N d F e B ) < / t d >< t d > – – – H z v i b . , Hz vib., Hz v ib . , k H z l i b r . < / t d > < t d > U p t o kHz libr.</td>
<td>Up to k Hz l ib r . < / t d >< t d > U pt o
Frequencies, materials, and Q-factors as reported in (Latorre et al., 2021 , Latorre et al., 2022 , 2002.03868 , Janse et al., 13 Aug 2024 ).
On-chip magnetic levitation platforms advance precision control of massive quantum objects, offer scalable integration with superconducting electronics, and support multi-dimensional sensing schemes. Their design relies on careful coil geometry, low-dissipation refrigeration, and detailed electromagnetic modeling; levitation regimes, frequency scaling, and noise performance are in quantitative agreement with analytic and finite-element models. Persistent-current operation, microwave-cavity coupling, and hybrid quantum-mechanical protocols are under development, solidifying this architecture's role in next-generation quantum technology and inertial measurement (Latorre et al., 2021 , Latorre et al., 2022 , 2002.03868 , Janse et al., 13 Aug 2024 ).
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